1 Step Equations With Fractions

To solve linear equations with fractions, we have to multiply the entire equation by the least common multiple to eliminate the fractions and then use the conventional method of solving start-caste equations.

In this commodity, nosotros will look at several examples with answers to master this topic and nosotros will likewise look at some practise issues and practice what we accept learned.

ALGEBRA

Relevant for…

Exploring linear equations with fractions examples and exercise problems.

Meet examples

ALGEBRA

Relevant for…

Exploring linear equations with fractions examples and practice issues.

Come across examples

Summary of linear equations with fractions

Remember that, for an equation to exist of the get-go degree, all the variables in the equation must have a maximum power of 1. For instance, the equations $latex \frac{1}{3}ten+two=six$ and $latex \frac{3}{2}ten=\frac{1}{two}x+10$ are linear equations with fractions. We can solve linear equations with fractions with the following steps:

Step 1: Remove the fractions: Nosotros multiply the entire equation by the to the lowest degree common multiple to remove the fractions.

Step two: Simplify: We remove the parentheses and other group signs and combine similar terms.

Pace 3: Solve for the variable: We utilize add-on and subtraction to motion the variable to only i side of the equation.

Step 4: Solve: We use multiplication and division to solve for the variable completely.

Solved examples of linear equations with fractions

EXAMPLE 1

Solve the equation $latex \frac{x}{3}+4=six$.

Solution

Stride 1: Remove the fractions: We multiply the unabridged equation by 3:

$$\frac{x}{3}+4=half-dozen$$

$latex x+4(3)=six(3)$

$latex x+12=18$

Stride 2: Simplify: We take null to simplify.

Step three: Solve for the variable: We subtract 12 from both sides of the equation:

$latex 10+12-12=18-12$

$latex x=6$

Pace 4: Solve: We have already got the answer:

$latex 10=6$

EXAMPLE 2

Detect the value often in the equation $latex \frac{10+1}{ii}+2=4$.

Solution

Step i: Remove the fractions: We multiply the entire equation by ii:

$$\frac{10+1}{ii}+two=4$$

$latex x+1+ii(two)=four(two)$

$latex x+1+4=eight$

Footstep 2: Simplify: Nosotros combine like terms:

$latex ten+one+4=viii$

$latex x+v=viii$

Pace three: Solve for the variable: Nosotros subtract 5 from both sides:

$latex x+5-5=8-5$

$latex ten=3$

Footstep 4: Solve: We have already got the answer:

$latex x=3$

Instance iii

Find the value ofx in the equation $latex \frac{2x+5}{3}+2x=7$.

Solution

Footstep 1: Remove the fractions: We multiply the entire equation past iii:

$$\frac{2x+5}{iii}+2x=7$$

$latex 2x+5+2x(three)=seven(iii)$

$latex 2x+5+6x=21$

Step two: Simplify: We combine like terms:

$latex 2x+5+6x=21$

$latex 8x+5=21$

Stride three: Solve for the variable: We decrease 5 from both sides:

$latex 8x+5-5=21-5$

$latex 8x=16$

Step four: Solve: We divide both sides by viii:

$$\frac{8x}{8}=\frac{16}{8}$$

$latex x=ii$

Case 4

Find the value ofx in the equation $latex \frac{3x-4}{4}+six=2x+10$.

Solution

Step one: Remove the fractions: We multiply the unabridged equation past iv:

$$\frac{3x-4}{4}+six=2x+10$$

$$3x-four+half dozen(4)=2x(four)+10(4)$$

$latex 3x-4+24=8x+xl$

Step 2: Simplify: Nosotros combine like terms:

$latex 3x-4+24=8x+40$

$latex 3x+xx=8x+twoscore$

Step 3: Solve for the variable: We subtract 20 and 8x from both sides of the equation:

$latex 3x+20-20=8x+40-20$

$latex 3x=8x+20$

$latex 3x-8x=8x+xx-8x$

$latex -5x=20$

Step 4: Solve: Nosotros divide both sides by -5:

$$\frac{-5x}{-5}=\frac{twenty}{-v}$$

$latex x=-four$

EXAMPLE five

Solve the equation $latex \frac{t+5}{two}+5=\frac{t-6}{3}+10$ fort.

Solution

Pace ane: Remove the fractions: Nosotros multiply the entire equation by vi:

$$\frac{t+5}{2}+5=\frac{t-6}{3}+10$$

$$3(t+5)+v(6)=2(t-half dozen)+x(6)$$

$latex 3(t+5)+30=2(t-6)+60$

Step 2: Simplify: We expand the parentheses and combine similar terms:

$latex 3(t+5)+30=ii(t-6)+threescore$

$latex 3t+15+30=2t-12+60$

$latex 3t+45=2t+48$

Step iii: Solve for the variable: Nosotros subtract 45 and twot from both sides:

$latex 3t+45-45=2t+48-45$

$latex 3t=2t+3$

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

$latex t=3$

Step 4: Solve: We already got the answer:

$latex t=3$

EXAMPLE half dozen

Solve the equation $latex \frac{5x-10}{2}+5=2(2x-two)+one$.

Solution

Step one: Remove the fractions: We multiply the entire equation by ii:

$$\frac{5x-10}{2}+five=2(2x-2)+i$$

$$5x-10+5(2)=two(2)(2x-2)+one(2)$$

$latex 5x-10+ten=iv(2x-ii)+2$

Pace ii: Simplify: We remove the parentheses and combine like terms:

$latex 5x-10+10=4(2x-2)+2$

$latex 5x-10+ten=8x-8+2$

$latex 5x=8x-half-dozen$

Step 3: Solve for the variable: We subtract 8x from both sides of the equation:

$latex 5x-8x=8x-6-8x$

$latex -3x=-6$

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

$$\frac{-3x}{-3}=\frac{-six}{-3}$$

$latex ten=2$

Instance 7

Find the value ofz from the equation $latex \frac{2z+1}{iii}+\frac{z-1}{2}=\frac{-3z-5}{2}-xi$.

Solution

Stride 1: Remove the fractions: We multiply the unabridged equation past six to eliminate all fractions:

$$\frac{2z+ane}{3}+\frac{z-1}{ii}=\frac{-3z-v}{ii}-11$$

$$2(2z+1)+three(z-one)=3(-3z-5)-6(11)$$

$$2(2z+1)+3(z-1)=3(-3z-5)-66$$

Stride 2: Simplify: Nosotros remove the parentheses and combine similar terms:

$$2(2z+one)+3(z-1)=3(-3z-5)-66$$

$latex 4z+2+3z-3=-9z-15-66$

$latex 7z-1=-9z-81$

Step three: Solve for the variable: Add together 1 and 9z from both sides of the equation:

$latex 7z-1+1=-9z-81+1$

$latex 7z=-9z-80$

$latex 7z+9z=-9z-80+9z$

$latex 16z=-lxxx$

Step four: Solve: Nosotros divide both sides by 16:

$$\frac{16z}{16}=\frac{-80}{16}$$

$latex x=-5$

Linear equations with fractions – Practise problems

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You accept completed the quiz!

Find the value of 10 in $latex \frac{2x-2}{3}+\frac{3x}{two}=-5$.

Write the answer in the input box.

ten=

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