Worksheet: Linear Equations with Variables on Both Sides

In this worksheet, we will practice solving equations in which the variable is on each side of the equation.

Q1:

Find the value of 𝑥: 4𝑥+5=1+5𝑥.

Q2:

Solve the equation 6(9𝑥2)4(7𝑥+1)=5(2𝑥4).

  • A 𝑥 = 7 2 3
  • B 𝑥 = 4 4 1
  • C 𝑥 = 1 6
  • D 𝑥 = 1 2 4

Q3:

Find the value of 𝑥 in 162𝑥=5𝑥+9.

Q4:

Solve the equation 7𝑥+9=22+4𝑥.

  • A 𝑥 = 1 3 3
  • B 𝑥 = 3 1 3
  • C 𝑥 = 3 1 1 1
  • D 𝑥 = 1 1 3 1

Q5:

Given that 6𝑥+𝑘+8=6𝑥2, find 𝑘.

Q6:

If 𝐽𝐾𝐿 is isosceles, where 𝐽𝐾𝐾𝐿, 𝐽𝐾=3𝑥+3, 𝐾𝐿=5𝑥3, and 𝐿𝐽=4𝑥+2, find the length of each side.

  • A 𝐽 𝐾 = 9 , 𝐾 𝐿 = 9 , 𝐿 𝐽 = 1 4
  • B 𝐽 𝐾 = 1 2 , 𝐾 𝐿 = 1 2 , 𝐿 𝐽 = 1 4
  • C 𝐽 𝐾 = 1 2 , 𝐾 𝐿 = 1 2 , 𝐿 𝐽 = 1 0
  • D 𝐽 𝐾 = 1 5 , 𝐾 𝐿 = 1 5 , 𝐿 𝐽 = 1 0
  • E 𝐽 𝐾 = 1 4 , 𝐾 𝐿 = 9 , 𝐿 𝐽 = 9

Q7:

𝑊 𝑋 𝑌 𝑍 is a rectangle where 𝑍𝑌=9𝑥8 and 𝑊𝑋=8𝑥+1. Find 𝑊𝑋.

Q8:

Find the value of 𝑥.

Q9:

Find the value of 𝑥: 212𝑥=3𝑥+16.

Q10:

Find the value of 𝑥: 7𝑥15=5𝑥3.

Q11:

Find the value of 𝑥: 12.6+4𝑥=9.6+8𝑥.

  • A 1 1 1 2 0
  • B 3 4
  • C 3 4
  • D 1 4
  • E 1 4

Q12:

Find the value of 𝑥 in 4.5+1.5𝑥=183𝑥.

Q13:

Find the solution set of the equation 53+𝑥3=13𝑥3.

  • A { 6 }
  • B { 2 }
  • C { 3 }
  • D { 4 }

Q14:

Find the solution set of the equation 41𝑎2=7+3𝑎.

  • A { 0 . 1 }
  • B { 5 }
  • C { 0 . 3 }
  • D { 0 . 4 }

Q15:

Given that 𝑚𝐵=𝑚𝐶, use the information in the figure to find the perimeter of triangle 𝐴𝐵𝐶.

Q16:

Mason and Jacob are going on vacation together. Mason has $400 and Jacob has $350. Given that, on average, Mason spends $28 and Jacob spends $26 per day, after how many days will they have the same amount of money left?

  • A25 days
  • B15 days
  • C50 days
  • D30 days
  • E13 days

Q17:

80 students decided to buy a present for their teacher. They split into two groups of 40. In the first group, each student gave 𝑥 dollars. In the second group, three-fifths of the students gave 23𝑥 dollars each, and the rest contributed a total of $288. Given that the two groups contributed the same amount, find the value of 𝑥.

  • A20
  • B36
  • C16
  • D26
  • E12

Q18:

Find the value of 𝐵𝐶 given the following information:

  • 𝐵 is on the line between 𝐴 and 𝐶.
  • 𝐴 𝐶 = ( 5 𝑥 + 9 ) i n c h e s .
  • 𝐴 𝐵 = ( 3 𝑥 1 ) i n c h e s .
  • 𝐵 𝐶 = ( 3 𝑥 + 4 ) i n c h e s .

Q19:

Point 𝑌 is the midpoint of segment 𝑋𝑍. Given that the length of 𝑋𝑌 is 4𝑥6, and that of 𝑌𝑍 is 182𝑥, what is the length of 𝑌𝑍?

Q20:

Solve 3(4𝑥12)+8=12𝑥6.

  • A 𝑥 = 1
  • B 𝑥 = 5
  • C 𝑥 = 5
  • DThere is an infinite number of solutions as the equation is always true.
  • EThere is no solution for 𝑥

Q21:

Find the value of 𝑛 in the equation 𝑛18+12=𝑛×18+16×12.

  • A 6
  • B 1 2
  • C 1 6
  • D 5 8
  • E2

Q22:

The startup cost for a restaurant is $120,000, and each meal costs $10 for the restaurant to make. If each meal is then sold for $15, after how many meals does the restaurant break even?

Q23:

Solve 𝑥+3(2𝑥+4)=7𝑥+4.

  • A 𝑥 = 2
  • B 𝑥 = 8
  • C 𝑥 = 2
  • DThere is no solution for 𝑥.
  • E 𝑥 = 8

Q24:

Solve 5𝑥+12=2𝑥6.

  • A 𝑥 = 1 8
  • B 𝑥 = 6
  • C 𝑥 = 3
  • D 𝑥 = 6
  • E 𝑥 = 3

Q25:

What is the value of 𝑎 if the equation 12𝑥=𝑎(𝑥+3) has no solutions?

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