Worksheet: Linear Equations with Variables on Both Sides

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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(9𝑥−2)−4(7𝑥+1)=−5(2𝑥−4).

  • A𝑥=−16
  • B𝑥=−441
  • C𝑥=124
  • D𝑥=−723

Q3:

Find the value of 𝑥 in 16−2𝑥=5𝑥+9.

Q4:

Solve the equation −7𝑥+9=−22+4𝑥.

  • A𝑥=3111
  • B𝑥=313
  • C𝑥=133
  • D𝑥=1131

Q5:

Given that 6𝑥+𝑘+8=6𝑥−2, find 𝑘.

Q6:

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

  • A𝐽𝐾=9, 𝐾𝐿=9, 𝐿𝐽=14
  • B𝐽𝐾=12, 𝐾𝐿=12, 𝐿𝐽=14
  • C𝐽𝐾=12, 𝐾𝐿=12, 𝐿𝐽=10
  • D𝐽𝐾=15, 𝐾𝐿=15, 𝐿𝐽=10
  • E𝐽𝐾=14, 𝐾𝐿=9, 𝐿𝐽=9

Q7:

𝑊𝑋𝑌𝑍 is a rectangle where 𝑍𝑌=9𝑥−8 and 𝑊𝑋=8𝑥+1. Find 𝑊𝑋.

Q8:

Find the value of 𝑥.

Q9:

Find the value of 𝑥: 2−12𝑥=3𝑥+16.

Q10:

Find the value of 𝑥: 7𝑥−15=5𝑥−3.

Q11:

Find the value of 𝑥: 12.6+4𝑥=9.6+8𝑥.

  • A−11120
  • B−34
  • C34
  • D−14
  • E14

Q12:

Find the value of 𝑥 in 4.5+1.5𝑥=18−3𝑥.

Q13:

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

  • 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 𝑚∠𝐵=𝑚∠𝐶, 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?

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 𝑥dollars. In the second group, three-fifths of the students gave 23𝑥dollars each, and the rest contributed a total of $288. Given that the two groups contributed the same amount, find the value of 𝑥.

Q18:

Find the value of 𝐵𝐶 given the following information:

  • 𝐵 is on the line between 𝐴 and 𝐶.
  • 𝐴𝐶=(5𝑥+9)inches.
  • 𝐴𝐵=(3𝑥−1)inches.
  • 𝐵𝐶=(3𝑥+4)inches.

Q19:

Point 𝑌 is the midpoint of segment 𝑋𝑍. Given that the length of 𝑋𝑌 is 4𝑥−6, and that of 𝑌𝑍 is 18−2𝑥, what is the length of 𝑌𝑍?

Q20:

Solve 3(4𝑥−12)+8=12𝑥−6.

  • A𝑥=1
  • B𝑥=5
  • C𝑥=−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
  • B12
  • C−16
  • D58
  • 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.

  • A𝑥=−2
  • B𝑥=8
  • C𝑥=2
  • DThere is no solution for 𝑥.
  • E𝑥=−8

Q24:

Solve 5𝑥+12=2𝑥−6.

  • A𝑥=−18
  • B𝑥=−6
  • C𝑥=−3
  • D𝑥=6
  • E𝑥=3

Q25:

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

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