20 Linear Equation Examples with Answers

Step 1: Simplify: We have nothing to simplify here.

Step 2: Solve for the variable: We use addition to solve for the variable:

$latex 5x-12=3$

$latex 5x-12+12=3+12$

$latex 5x=15$

Step 3: Solve: We divide both sides by 5:

$$\frac{5x}{5}=\frac{15}{5}$$

$latex x=3$

Step 1: Simplify: We have nothing to simplify.

Step 2: Solve for the variable: We use addition and subtraction to solve for the variable:

$latex 3x+1=x-3$

$latex 3x+1-1=x-3-1$

$latex 3x=x-4$

$latex 3x-x=x-4-x$

$latex 2x=-4$

Step 3: Solve: We divide both sides by 2:

$$\frac{2x}{2}=\frac{-4}{2}$$

$latex x=-2$

Step 1: Simplify: We do not have like terms.

Step 2: Solve for the variable: We use subtraction to solve for the variable:

$latex 5t+5=3t+7$

$latex 5t+5-5=3t+7-5$

$latex 5t=3t+2$

$latex 5t-3t=3t+2-3t$

$latex 2t=2$

Step 3: Solve: We divide both sides by 2:

$$\frac{2t}{2}=\frac{2}{2}$$

$latex t=1$

Step 1: Simplify: We expand the parentheses:

$latex 3(2x+1)=-9$

$latex 6x+3=-9$

Step 2: Solve for the variable: We use subtraction to solve for the variable:

$latex 6x+3=-9$

$latex 6x+3-3=-9-3$

$latex 6x=-12$

Step 3: Solve: We divide both sides by 6:

$$\frac{6x}{6}=\frac{-12}{6}$$

$latex x=-2$

Step 1: Simplify: We expand the parentheses on both sides of the equation and combine like terms:

$latex 2(2x-5)=3(x-1)-4$

$latex 4x-10=3x-3-4$

$latex 4x-10=3x-7$

Step 2: Solve for the variable: We use addition and subtraction to solve for the variable:

$latex 4x-10+10=3x-7+10$

$latex 4x=3x+3$

$latex 4x-3x=3-3x$

$latex x=3$

Step 3: Solve: In this case, we no longer have to divide:

$latex x=3$

Step 1: Simplify: We expand the parentheses and combine like terms:

$latex 3(z-2)+10=2(2z+2)+2$

$latex 3z-6+10=4z+4+2$

$latex 3z+4=4z+6$

Step 2: Solve for the variable: We use subtraction to solve for the variable:

$latex 3z+4-4=4z+6-4$

$latex 3z=4z+2$

$latex 3z-4z=2$

$latex -z=2$

Step 3: Solve: We divide both sides by -1:

$$\frac{-z}{-1}=\frac{2}{-1}$$

$latex z=-2$

Step 1: Simplify: We multiply by 3 to eliminate the fraction:

$$\frac{2x+1}{3}=x-1$$

$latex 2x+1=3x-3$

Step 2: Solve for the variable: We subtract 1 and 3x from both sides:

$latex 2x+1=3x-3$

$latex 2x+1-1=3x-3-1$

$latex 2x=3x-4$

$latex 2x-3x=3x-4-3x$

$latex -x=-4$

Step 3: Solve: We divide both sides by -1:

$$\frac{-x}{-1}=\frac{-4}{-1}$$

$latex x=4$

Step 1: Simplify: We multiply both sides of the equation by 3 to eliminate the fractions and combine like terms:

$$\frac{4x}{3}-2=\frac{2x+3}{3}-1$$

$latex 4x-6=2x+3-3$

$latex 4x-6=2x$

Step 2: Solve for the variable: We add 6 and subtract 2x from both sides:

$latex 4x-6+6=2x+6$

$latex 4x=2x+6$

$latex 4x-2x=2x+6-2x$

$latex 2x=6$

Step 3: Solve: We divide both sides by 2:

$$\frac{2x}{2}=\frac{6}{2}$$

$latex x=3$

Step 1: Simplify: We multiply by 15 to eliminate the fractions and combine like terms:

$$\frac{2t-5}{5}+2=\frac{t-2}{3}+2$$

$$3(2t-5)+15(2)=5(t-2)+15(2)$$

$latex 6t-15+30=5t-10+30$

$latex 6t+15=5t+20$

Step 2: Solve for the variable: We subtract 15 and 5 t from both sides:

$latex 6t+15=5t+20$

$latex 6t+15-15=5t+20-15$

$latex 6t=5t+5$

$latex 6t-5t=5t+5-5t$

$latex t=5$

Step 3: Solve: We no longer have to divide:

$latex t=5$

Step 1: Simplify: We multiply both sides by (x+1) and combine like terms:

$$\frac{2x-3}{x+1}+2=3$$

$latex 2x-3+2(x+1)=3(x+1)$

$latex 2x-3+2x+2=3x+3$

$latex 4x-1=3x+3$

Step 2: Solve for the variable: Add 1 and subtract 3 x from both sides:

$latex 4x-1=3x+3$

$latex 4x-1+1=3x+3+1$

$latex 4x=3x+4$

$latex 4x-3x=3x+4-3x$

$latex x=4$

Step 3: Solve: We no longer have to divide:

$latex x=4$

Step 1: Simplify: We expand the parentheses and combine like terms:

$latex 3t+4(t-10)=t+20$

$latex 3t+4t-40=t+20$

$latex 7t-40=t+20$

Step 2: Solve for the variable: We add 40 and subtract t from both sides:

$latex 7t-40=t+20$

$latex 7t-40+40=t+20+40$

$latex 7t=t+60$

$latex 7t-t=t+60-t$

$latex 6t=60$

Step 3: Solve: We divide both sides by 6:

$$\frac{6t}{6}=\frac{60}{6}$$

$latex t=10$

Step 1: Simplify: We expand the parentheses and combine like terms:

$latex 3x+6(x+1)=3(x+1)+5$

$latex 3x+6x+6=3x+3+5$

$latex 9x+6=3x+8$

Step 2: Solve for the variable: We subtract 6 and 3 x from both sides:

$latex 9x+6=3x+8$

$latex 9x+6-6=3x+8-6$

$latex 9x=3x+2$

$latex 9x-3x=3x+2-3x$

$latex 6x=2$

Step 3: Solve: We divide both sides by 6:

$$\frac{6x}{6}=\frac{2}{6}$$

$$x=\frac{1}{3}$$

Step 1: Simplify: We multiply the entire equation by 4 (x+2) and combine like terms:

$$\frac{1}{x+2}+2=\frac{9}{4}$$

$latex 4+8(x+2)=9(x+2)$

$latex 4+8x+16=9x+18$

$latex 8x+20=9x+18$

Step 2: Solve for the variable: We subtract 20 and 9 x from both sides:

$latex 8x+20-20=9x+18-20$

$latex 8x=9x-2$

$latex 8x-9x=9x-2-9x$

$latex -x=-2$

Step 3: Solve: We divide both sides by -1:

$$\frac{-x}{-1}=\frac{-2}{-1}$$

$latex x=2$

Step 1: Simplify: We expand the parentheses and combine like terms:

$$2y+3(2y-5)+4=y+3(2y-2)-6$$

$latex 2y+6y-15+4=y+6y-6-6$

$latex 8y-11=7y-12$

Step 2: Solve for the variable: We add 11 and subtract 7y from both sides:

$latex 8y-11=7y-12$

$latex 8y-11+11=7y-12+11$

$latex 8y=7y-1$

$latex 8y-7y=7y-1-7y$

$latex y=-1$

Step 3: Solve: We no longer have to divide:

$latex y=-1$

Step 1: Simplify: We multiply the entire equation by 3, expand the parentheses, and combine like terms:

$$\frac{4x-9}{3}+2=3(x-2)$$

$latex 4x-9+6=9(x-2)$

$latex 4x-3=9x-18$

Step 2: Solve for the variable: We add 3 and subtract 9 x from both sides:

$latex 4x-3+3=9x-18+3$

$latex 4x=9x-15$

$latex 4x-9x=9x-15-9x$

$latex -5x=-15$

Step 3: Solve: We divide both sides by -5:

$$\frac{-5x}{-5}=\frac{-15}{-5}$$

$latex x=3$

Step 1: Simplify: We expand the parentheses and combine like terms:

$latex -3x+18=-x(13-10)+4x-2$

$latex -3x+18=-x(3)+4x-2$

$latex -3x+18=-3x+4x-2$

$latex -3x+18=x-2$

Step 2: Solve for the variable: We subtract 18 and subtract x from both sides:

$latex -3x+18-18=x-2-18$

$latex -3x=x-20$

$latex -3x-x=x-20-x$

$latex -4x=-20$

Step 3: Solve: We divide both sides by -4:

$$\frac{-4x}{-4}=\frac{-20}{-4}$$

$latex x=5$

Step 1: Simplify: We expand the parentheses and combine like terms:

$latex 10(2w-5)=2w+2(w+1)$

$latex 20w-50=2w+2w+2$

$latex 20w-50=4w+2$

Step 2: Solve for the variable: We add 50 and subtract 4 w from both sides:

$latex 20w-50=4w+2$

$latex 20w-50+50=4w+2+50$

$latex 20w=4w+52$

$latex 20w-4w=4w+52-4w$

$latex 16w=52$

Step 3: Solve: We divide both sides by 16 and simplify the fraction:

$$\frac{16w}{16}=\frac{52}{16}$$

$$x=\frac{13}{4}$$

Step 1: Simplify: We multiply both sides by 2 to eliminate the fraction, expand the parentheses, and combine like terms:

$$3(-2r-5)+4=\frac{r}{2}+2$$

$latex 6(-2r-5)+8=r+4$

$latex -12r-30+8=r+4$

$latex -12r-22=r+4$

Step 2: Solve for the variable: We add 22 and subtract r from both sides:

$latex -12r-22=r+4$

$latex -12r-22+22=r+4+22$

$latex -12r=r+26$

$latex -12r-r=r+26-r$

$latex -13r=26$

Step 3: Solve: We divide both sides by -13:

$$\frac{-13r}{-13}=\frac{26}{-13}$$

$latex x=-2$

Step 1: Simplify: We expand all the parentheses and combine like terms:

$$3x+4(-2x+1)=3(x-5)+2(2x-7)-3$$

$$ 3x-8x+4=3x-15+4x-14-3$$

$latex -5x+4=7x-32$

Step 2: Solve for the variable: We subtract 4 and 7 x from both sides:

$latex -5x+4-4=7x-32-4$

$latex -5x=7x-36$

$latex -5x-7x=7x-36-7x$

$latex -12x=-36$

Step 3: Solve: We divide both sides by -12:

$$\frac{-12x}{-12}=\frac{-36}{-12}$$

$latex x=3$

Step 1: Simplify: We start by simplifying the fraction, then multiply by 4 to eliminate the fractions and combine like terms:

$$2\left( \frac{x+2}{4}\right)+2=\frac{3x}{4}+2$$

$$\frac{x+2}{2}+2=\frac{3x}{4}+2$$

$latex 2(x+2)+8=3x+8$

$latex 2x+4+8=3x+8$

$latex 2x+12=3x+8$

Step 2: Solve for the variable: We subtract 12 and 3 x from both sides:

$latex 2x+12-12=3x+8-12$

$latex 2x=3x-4$

$latex 2x-3x=3x-4-3x$

$latex -x=-4$

Step 3: Solve: We divide both sides by -1:

$$\frac{-x}{-1}=\frac{-4}{-1}$$

$latex x=4$