Practice set adapted from the handout “Solving Linear Equations.” Problems include one-step, two-step, distributive, decimals, fractions, and special cases (no solution / all real numbers). Answers can be revealed after you try.
How to solve (quick recap)
Simplify both sides (distribute, combine like terms).
Move variable terms to one side and constants to the other.
Undo multiplication/division to isolate the variable.
Check your solution in the original equation.
Practice Set
Type your answer for x. For “no solution” type none. For “all real numbers” type all.
#1.4x = 4
Hint
Divide both sides by 4 to isolate x.
#2.x - 6 = -7
Hint
Add 6 to both sides to isolate x.
#3.x + 4 = 15
Hint
Subtract 4 from both sides to isolate x.
#4.x/3 = -9
Hint
Multiply both sides by 3 to isolate x.
#5.2x = 4
Hint
Divide both sides by 2 to isolate x.
#6.14 = 3 + 2x
Hint
Subtract 3 from both sides, then divide by 2 to isolate x.
#7.8x + 3 = -19
Hint
Subtract 3 from both sides, then divide by 8 to isolate x.
#8.6 - x = 9
Hint
Subtract 6 from both sides, then multiply by -1 to isolate x.
#9.-x = -12
Hint
Multiply both sides by -1 to isolate x.
#10.3x + 2x = 6
Hint
Combine the x terms on the left side, then divide by the coefficient of x.
#11.3(x+2) = 9
Hint
Distribute the 3 on the left side, subtract the constant term, then divide by the coefficient of x.
#12.4(x-6) + 2x = 0
Hint
Distribute the 4, combine the x terms, add the constant to the other side, then divide by the coefficient of x.
#13.3x - 2x + 6 = -15
Hint
Combine the x terms, subtract 6 from both sides, then isolate x.
#14.4 - 2(x+1) = 3x
Hint
Distribute the -2 on the left, move all x terms to one side and constants to the other, then divide by the coefficient of x.
#15.27 - 46 = 2x - x
Hint
Simplify the left side by subtracting 46 from 27, combine the x terms on the right, then isolate x.
#16.4x + 6 = 7x + 9 - 18
Hint
Simplify the right side by combining 9 and -18, move all x terms to one side and constants to the other, then divide by the coefficient of x.
#17.4 - 3(x-2) = 10
Hint
Distribute the -3, combine constants on the left, subtract 10 from both sides, then divide by the coefficient of x.
#18.-3 + 3x = -2(x-1)
Hint
Distribute the -2 on the right, move all x terms to one side and constants to the other, then divide by the coefficient of x.
#19.9x + 6 = -3x + 30
Hint
Add 3x to both sides to get all x terms on one side, subtract 6 from both sides, then divide by the coefficient of x.
#20.x/2 + 2x = 6
Hint
Rewrite x/2 + 2x as a single fraction with a common denominator, multiply both sides by that denominator, then divide by the coefficient of x.
#21.2x + 6 = 3x + 12
Hint
Subtract 2x from both sides, subtract 12 from both sides, then isolate x.
#22.-5x + 3 = 2x + 10
Hint
Add 5x to both sides, subtract 10 from both sides, then divide by the coefficient of x.
#23.3x - 12x = 24 - 9x
Hint
Combine the x terms on both sides. If the x terms cancel out, check if the remaining equation is true or false.
#24.2(x-2) + 4x = -3(x-5)
Hint
Distribute the 2 and -3, combine like terms on the left, move all x terms to one side and constants to the other, then divide by the coefficient of x.
#25.4(x+2) - 3x = 4 - 8x + 8
Hint
Distribute the 4, combine like terms on both sides, move all x terms to one side and constants to the other, then divide by the coefficient of x.
#26.6x + 11 = x(6) + 5x
Hint
Rewrite x(6) as 6x, combine like terms on the right, move all x terms to one side and constants to the other, then divide by the coefficient of x.
#27.2x + 7x = 6x + 9 + 4x
Hint
Combine x terms on both sides, move all x terms to one side, then isolate x.
#28.-5x/3 + 4(x-2) = -6 + 20x - 9
Hint
Distribute the 4, combine constants on the right, multiply through by 3 to clear the fraction, move all x terms to one side and constants to the other, then divide by the coefficient of x.
#29.4(x+1) - 3x - (x+5) = 0
Hint
Distribute the 4 and -1, combine all x terms and constants. If the x terms cancel, check if the resulting equation is true or false.
#30.-2(x+4) + (x-6) - (2x-3) = 0
Hint
Distribute the -2 and -1, combine all x terms and constants, move the constant to the other side, then divide by the coefficient of x.
#31.x/4 = 12
Hint
Multiply both sides by 4 to isolate x.
#32.(x/5) + 2 = 5
Hint
Subtract 2 from both sides, then multiply by 5 to isolate x.
#33.0.05x + 0.25 = 0.2
Hint
Subtract 0.25 from both sides, then divide by 0.05 (or multiply by 20) to isolate x.
#34.0.5(x+3) = 6
Hint
Distribute the 0.5, subtract the constant term, then divide by 0.5 (or multiply by 2) to isolate x.
#35.(x/3) + (x/6) = 5
Hint
Use a common denominator (6) to combine the fractions, multiply both sides by 6, then divide by the coefficient of x.
#36.(2/3)x - (1/2) = 3
Hint
Add 1/2 to both sides, then multiply both sides by the reciprocal of 2/3 to isolate x.
#37.10 - 5x + 3(x-4) = 2(x-7)
Hint
Distribute the 3 and 2, combine like terms on both sides, move all x terms to one side and constants to the other, then divide by the coefficient of x.
#38.0.25(60x) + 0.1x = 0.15(60 - x)
Hint
Distribute 0.25 and 0.15, combine like terms on both sides, move all x terms to one side, then divide by the coefficient of x.
#39.3(2x-4) = 18
Hint
Distribute the 3, add the constant to both sides, then divide by the coefficient of x.
#40.(x-3)/2 + (x+1)/3 = 5
Hint
Multiply through by 6 to clear the fractions, distribute where needed, combine like terms, then divide by the coefficient of x.