Lesson Worksheet: Linear Equations with Variables on Both Sides Mathematics • 8th Grade

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

Q1:

Find the value of π‘₯: 4π‘₯+5=1+5π‘₯.

Q2:

Solve the equation βˆ’6(9π‘₯βˆ’2)βˆ’4(7π‘₯+1)=βˆ’5(2π‘₯βˆ’4).

  • Aπ‘₯=βˆ’16
  • Bπ‘₯=βˆ’441
  • Cπ‘₯=124
  • Dπ‘₯=βˆ’723

Q3:

Find the value of π‘₯ in 16βˆ’2π‘₯=5π‘₯+9.

Q4:

Solve the equation βˆ’7π‘₯+9=βˆ’22+4π‘₯.

  • Aπ‘₯=3111
  • Bπ‘₯=313
  • Cπ‘₯=133
  • Dπ‘₯=1131

Q5:

Given that 6π‘₯+π‘˜+8=6π‘₯βˆ’2, find π‘˜.

Q6:

If △𝐽𝐾𝐿 is isosceles, where 𝐽𝐾≅𝐾𝐿, 𝐽𝐾=3π‘₯+3, 𝐾𝐿=5π‘₯βˆ’3, and 𝐿𝐽=4π‘₯+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:

π‘Šπ‘‹π‘Œπ‘ is a rectangle where π‘π‘Œ=9π‘₯βˆ’8 and π‘Šπ‘‹=8π‘₯+1. Find π‘Šπ‘‹.

Q8:

Find the value of π‘₯.

Q9:

Find the value of π‘₯: 2βˆ’12π‘₯=3π‘₯+16.

Q10:

Find the value of π‘₯: 7π‘₯βˆ’15=5π‘₯βˆ’3.

Q11:

Find the value of π‘₯: 12.6+4π‘₯=9.6+8π‘₯.

  • Aβˆ’11120
  • Bβˆ’34
  • C34
  • Dβˆ’14
  • E14

Q12:

Find the value of π‘₯ in 4.5+1.5π‘₯=18βˆ’3π‘₯.

Q13:

Find the solution set of the equation βˆ’53+π‘₯3=13βˆ’π‘₯3.

  • A{6}
  • B{2}
  • C{3}
  • D{4}

Q14:

Find the solution set of the equation 41π‘Ž2=7+3π‘Ž.

  • A{0.1}
  • B{5}
  • C{0.3}
  • D{0.4}

Q15:

Given that π‘šβˆ π΅=π‘šβˆ πΆ, use the information in the figure to find the perimeter of triangle 𝐴𝐡𝐢.

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

Q18:

Find the value of 𝐡𝐢 given the following information:

  • 𝐡 is on the line between 𝐴 and 𝐢.
  • 𝐴𝐢=(5π‘₯+9)inches.
  • 𝐴𝐡=(3π‘₯βˆ’1)inches.
  • 𝐡𝐢=(3π‘₯+4)inches.

Q19:

Point π‘Œ is the midpoint of segment 𝑋𝑍. Given that the length of π‘‹π‘Œ is 4π‘₯βˆ’6, and that of π‘Œπ‘ is 18βˆ’2π‘₯, what is the length of π‘Œπ‘?

Q20:

Solve 3(4π‘₯βˆ’12)+8=12π‘₯βˆ’6.

  • Aπ‘₯=1
  • Bπ‘₯=5
  • Cπ‘₯=βˆ’5
  • DThere is an infinite number of solutions as the equation is always true.
  • EThere is no solution for π‘₯

Q21:

Find the value of 𝑛 in the equation 𝑛18+12=𝑛×18+βˆ’16Γ—12.

  • Aβˆ’6
  • B12
  • Cβˆ’16
  • D58
  • E2

Q22:

Solve π‘₯+3(2π‘₯+4)=7π‘₯+4.

  • Aπ‘₯=βˆ’2
  • Bπ‘₯=8
  • Cπ‘₯=2
  • DThere is no solution for π‘₯.
  • Eπ‘₯=βˆ’8

Q23:

Solve 5π‘₯+12=2π‘₯βˆ’6.

  • Aπ‘₯=βˆ’18
  • Bπ‘₯=βˆ’6
  • Cπ‘₯=βˆ’3
  • Dπ‘₯=6
  • Eπ‘₯=3

Q24:

The equation 2π‘₯+10=5π‘₯+5 can be solved in three steps. Which of the following is NOT a valid first step of such a method?

  • ATake away 5π‘₯ from both sides.
  • BTake away 5 from both sides.
  • CDivide both sides by 5.
  • DTake away 2π‘₯ from both sides.
  • ETake away 10 from both sides.

Q25:

Solve 8βˆ’2ο€Ό3π‘₯2+4=βˆ’5π‘₯+2.

  • Aπ‘₯=1
  • Bπ‘₯=βˆ’2
  • Cπ‘₯=βˆ’4
  • Dπ‘₯=4
  • Eπ‘₯=βˆ’1

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