Solving Equations with Rational Coefficients Solve the following equations with rational coefficients. Show all work and CHECK! 1) 1.5 โ 1.2 โ = 0.5 2) 5.85 = 8.68 + 3.68 3) 4.93 โ 9.2 = 0.66 4) 7.6 + 9.6 = 1.2 5) ! ! + ! ! = 2 6) ! ! โ ! ! = โ3 7) โ ! !" + ! ! = ! ! 8) ! !" โ = ! ! โ ! ! 9) ! ! โ ! ! = !" ! + ! ! 10) โ4.42 + 0.9 = โ9.070 โ 0.432 11) 0.025 + 4 = 1.2415 12) ! ! + ! !" = !" !" + ! ! 13) 6 ! ! โ ! ! = ! !" 14) 5 ! !" โ 0.2 = ! ! + 0.8 15) ! ! โ 3 + 0.625 = 5 16) 2.25 โ 3 = 0.375 โ ! ! 17) ! !! โ ! ! = ! ! 18) ! !! = ! !! โ ! !" 19) 1.8 โ ! !! = ! !"! 20) 3 ! ! โ ! !! = 6( ! ! + 3) 21) At a basketball game, you buy 10 raffle tickets. Your friend buys a T-shirt for $13.50 and 1 raffle ticket. If you each spend the same amount, write and solve an equation that will help you find the cost, x, of one ticket. 22) At the deli, Swiss cheese costs $3.96 per pound and turkey costs $4.76 per pound. You buy the same amount of each and spend $13.08. Write and solve an equation to find how many pounds of each you buy. 23) You buy clothes pattern for $7 at a fabric store. You also buy ! ! yard of red fabric, 2 ! ! yards of purple fabric, and ! ! yard of blue fabric. The total cost is $23.50. All three fabrics cost the same per yard. Write and solve an equation to find the price per yard. 24) You mow ! ! of the lawn, and your sister mows ! ! of the lawn. What is the area of the entire lawn? What is the length of the section left to mow? 25) The length of a rectangle is 2 ! ! times the width. The perimeter of the rectangle is 2 ! ! units less than 3 times the length. Find the width and the area of the rectangle. Solving Equations with Rational Coefficients Checklist: I can use the Distributive Property to get rid of parentheses on each side of the equation. I can combine like terms on the same side of the equation. I can perform inverse operations on like terms by undoing addition and subtraction first. I can perform inverse operations on like terms by undoing multiplication and division second. I can check my answer by substituting the value into the equation. Solving Equations with Rational Coefficients Solve the following equations with rational coefficients. Show all work and CHECK! 1) 1.5 โ 1.2 โ = 0.5 2) 5.85 = 8.68 + 3.68 3) 4.93 โ 9.2 = 0.66 4) 7.6 + 9.6 = 1.2 5) ! ! + ! ! = 2 6) ! ! โ ! ! = โ3 7) โ ! !" + ! ! = ! ! 8) ! !" โ = ! ! โ ! ! 9) ! ! โ ! ! = !" ! + ! ! 10) โ4.42 + 0.9 = โ9.070 โ 0.432 11) 0.025 + 4 = 1.2415 12) ! ! + ! !" = !" !" + ! ! 13) 6 ! ! โ ! ! = ! !" 14) 5 ! !" โ 0.2 = ! ! + 0.8 15) ! ! โ 3 + 0.625 = 5 16) 2.25 โ 3 = 0.375 โ ! ! 17) ! !! โ ! ! = ! ! 18) ! !! = ! !! โ ! !" 19) 1.8 โ ! !! = ! !"! 20) 3 ! ! โ ! !! = 6( ! ! + 3) 21) At a basketball game, you buy 10 raffle tickets. Your friend buys a T-shirt for $13.50 and 1 raffle ticket. If you each spend the same amount, write and solve an equation that will help you find the cost, x, of one ticket. 22) At the deli, Swiss cheese costs $3.96 per pound and turkey costs $4.76 per pound. You buy the same amount of each and spend $13.08. Write and solve an equation to find how many pounds of each you buy. 23) You buy clothes pattern for $7 at a fabric store. You also buy ! ! yard of red fabric, 2 ! ! yards of purple fabric, and ! ! yard of blue fabric. The total cost is $23.50. All three fabrics cost the same per yard. Write and solve an equation to find the price per yard. 24) You mow ! ! of the lawn, and your sister mows ! ! of the lawn. What is the area of the entire lawn? What is the length of the section left to mow? 25) The length of a rectangle is 2 ! ! times the width. The perimeter of the rectangle is 2 ! ! units less than 3 times the length. Find the width and the area of the rectangle. Solving Equations with Rational Coefficients Checklist: I can use the Distributive Property to get rid of parentheses on each side of the equation. I can combine like terms on the same side of the equation. I can perform inverse operations on like terms by undoing addition and subtraction first. I can perform inverse operations on like terms by undoing multiplication and division second. I can check my answer by substituting the value into the equation.
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Solving Equations with Rational Coefficients Solve the following equations with rational coefficients. Show all work and CHECK! 1) 1.5๐ โ 1.2 โ ๐ = 0.5
2) 5.85๐ = 8.68 + 3.68๐
3) 4.93 โ 9.2๐ฃ = 0.66๐ฃ
4) 7.6๐ + 9.6 = 1.2๐
5) !!๐ + !
!= 2๐
6) !
!โ !
!๐ = โ3๐
7) โ !
!"๐ + !
!= !
!๐
8) !
!"โ ๐ค = !
!โ !
!๐ค
9) !
!๐ง โ !
!= !"
!+ !
!๐ง
10) โ4.42๐ฅ + 0.9 = โ9.070 โ 0.432๐ฅ
11) 0.025 ๐ฅ + 4 = 1.2415
12) !!+ !
!"๐ = !"
!"+ !
!๐
13) 6 !
!๐ โ !
!= !
!"๐
14) 5 !
!"โ 0.2๐ฅ = !
!๐ฅ + 0.8
15) !
!๐ฅ โ 3 + 0.625๐ฅ = 5
16) 2.25 โ 3๐ง = 0.375 โ !
!๐ง
17) !
!!โ !
!= !
!
18) !
!!= !
!!โ !
!"
19) 1.8 โ !
!!= !
!"!
20) 3 !
!โ !
!!= 6(!
!+ 3)
21) At a basketball game, you buy 10 raffle
tickets. Your friend buys a T-shirt for $13.50 and 1 raffle ticket. If you each spend the same amount, write and solve an equation that will help you find the cost, x, of one ticket.
22) At the deli, Swiss cheese costs $3.96 per pound and turkey costs $4.76 per pound. You buy the same amount of each and spend $13.08. Write and solve an equation to find how many pounds of each you buy.
23) You buy clothes pattern for $7 at a fabric store. You also buy !
! yard of red fabric, 2 !
!
yards of purple fabric, and !! yard of blue
fabric. The total cost is $23.50. All three fabrics cost the same per yard. Write and solve an equation to find the price per yard.
24) You mow !
! of the lawn, and your sister mows !
! of the lawn. What is the
area of the entire lawn? What is the length of the section left to mow?
25) The length of a rectangle is 2 !! times the width. The perimeter of the
rectangle is 2 !! units less than 3 times the length. Find the width and the
area of the rectangle.
Solving Equations with Rational Coefficients Checklist: รพ I can use the Distributive Property to get rid of parentheses on each side of the equation. รพ I can combine like terms on the same side of the equation. รพ I can perform inverse operations on like terms by undoing addition and subtraction first. รพ I can perform inverse operations on like terms by undoing multiplication and division second. รพ I can check my answer by substituting the value into the equation. Solving Equations with Rational Coefficients Solve the following equations with rational coefficients. Show all work and CHECK! 1) 1.5๐ โ 1.2 โ ๐ = 0.5
2) 5.85๐ = 8.68 + 3.68๐
3) 4.93 โ 9.2๐ฃ = 0.66๐ฃ
4) 7.6๐ + 9.6 = 1.2๐
5) !!๐ + !
!= 2๐
6) !
!โ !
!๐ = โ3๐
7) โ !
!"๐ + !
!= !
!๐
8) !
!"โ ๐ค = !
!โ !
!๐ค
9) !
!๐ง โ !
!= !"
!+ !
!๐ง
10) โ4.42๐ฅ + 0.9 = โ9.070 โ 0.432๐ฅ
11) 0.025 ๐ฅ + 4 = 1.2415
12) !!+ !
!"๐ = !"
!"+ !
!๐
13) 6 !
!๐ โ !
!= !
!"๐
14) 5 !
!"โ 0.2๐ฅ = !
!๐ฅ + 0.8
15) !
!๐ฅ โ 3 + 0.625๐ฅ = 5
16) 2.25 โ 3๐ง = 0.375 โ !
!๐ง
17) !
!!โ !
!= !
!
18) !
!!= !
!!โ !
!"
19) 1.8 โ !
!!= !
!"!
20) 3 !
!โ !
!!= 6(!
!+ 3)
21) At a basketball game, you buy 10 raffle
tickets. Your friend buys a T-shirt for $13.50 and 1 raffle ticket. If you each spend the same amount, write and solve an equation that will help you find the cost, x, of one ticket.
22) At the deli, Swiss cheese costs $3.96 per pound and turkey costs $4.76 per pound. You buy the same amount of each and spend $13.08. Write and solve an equation to find how many pounds of each you buy.
23) You buy clothes pattern for $7 at a fabric store. You also buy !
! yard of red fabric, 2 !
!
yards of purple fabric, and !! yard of blue
fabric. The total cost is $23.50. All three fabrics cost the same per yard. Write and solve an equation to find the price per yard.
24) You mow !
! of the lawn, and your sister mows !
! of the lawn. What is the
area of the entire lawn? What is the length of the section left to mow?
25) The length of a rectangle is 2 !! times the width. The perimeter of the
rectangle is 2 !! units less than 3 times the length. Find the width and the
area of the rectangle.
Solving Equations with Rational Coefficients Checklist: รพ I can use the Distributive Property to get rid of parentheses on each side of the equation. รพ I can combine like terms on the same side of the equation. รพ I can perform inverse operations on like terms by undoing addition and subtraction first. รพ I can perform inverse operations on like terms by undoing multiplication and division second. รพ I can check my answer by substituting the value into the equation.
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