Step-by-Step: Linear Equations Involving Fractions with solved questions. |#SAT, WASSCE AND BECE|, |#PDF AND VIDEOS|

linear equations involving fractions can look confusing at first, but they follow the same basic steps as regular linear equations. with just a few extra tricks in this post, we will break down how to solve these types of equations step-by-step, using clear examples and explanations in both video and pdf files. whether you are preparing for SAT, WASSCE, OR BSSCE final examination or just brushing up for your mathematics skills, this guide will help you understand and master fractional linear equations with ease. when the equation includes fractions, we call it a linear equation with fractions.

Steps to solve linear equations involving fractions:

Example;

Find the truth set of \[\frac{1}{5}(4x-1)=\frac{1}{3}(2x+1)\]

1. Find the lowest common multiples of all denominators in the equation. this will then clear the equation of fraction and then proceed.

the lowest common multiple of 5 and 3 is 15 since 5 and 3 can divide 15 perfectly

2. Multiply the L.C.M of the denominators by every term to eliminate the denominators of the fractions.

\[ 15 \times \frac{1}{5}(4x-1)=15 \times \frac{1}{3}(2x+1)\] the denominator 15/5 = 3 and the second denominator 15/3 = 5. Therefore multiple first bracket by 3 and second bracket by 5

3. Clear the equations of the bracket (if any) by multiplying the any variable or number outside a bracket.

\[3(4x-1)=5(2x+1)\]

4. Grouping like terms- let same variables be one side of the equation and the numbers too one side.

\[12x-3 = 10x + 5\] Subtracting 10x from both sides and addinG 3 to both sides \[12x-3-10x+3=10x+5-10x+3\] \[2x=8\]

5. Find the value of the letter (variable) in the equation by simplifying both side of the equation.

\[\frac{2x}{2}=\frac{8}{2}\] 2 cancel 2 and 2 enter 8, 4 times Therefore x=4

Below are details step-by-step solved linear equation involving fractions and Past questions with answers for WASSCE, SAT, BECE and BSSCE.

1. \[\frac{x-1}{2}+3x=10\] Since the equation has only one fraction, use the denominator of the fraction to multiple each term in the equation. \[2\times\frac{x-1}{2}+2(3x)=2×10\] Multiple each term by 2 to clear of the fraction part. \[(x-1)+6x=20\] Multiple the bracket by 1 \[x-1+6x=20\] Grouping like terms. Add 1 to both sides. \[x-1+6x+1=20+1\] \[7x=21\] Divide both sides by 7 \[\frac{7x}{7}=\frac{21}{7}\] Therefore \[x=3\] Question.2 \[4:(x+5)=1:2\]

Solve for x.

Step 1

since the equation is in the form of ratio, and the ratio can be written as fraction.

Thus; \[\frac{4}{x+5}=\frac{1}{2}\] Step.2

Find the L.C.M of x+5 and 2

Taking 2(x+5) as the LCM is perfect because all the 28 denominators, 2 and x+5 can divide (enter) 2(x+5) perfectly.

Step.3

Multiply each fraction in the equation by 2(x+5). \[2(x+5)\times\frac{4}{(x+5}=2(x+5)\times\frac{1}{2}\] Using the denominator of each fraction to divide the L.C.M 2(x+5). \[2(4)=1(x+5)\] \[8=x+5\] Grouping like terms, subtract 5 from the both sides of the equation. \[8-5=x+5-5\] \[3=x\] Therefore x=3

Solve the following tricky passed questions on linear equation involving fractions for SAT,WASSCE and BECE final students

How do find the value of x in the following math pasco using the easy to follow guides above

Q.1 \[\frac{1}{3}x+\frac{1}{5}x=\frac{2}{3}(x+2)\] Q.2 \[\frac{3x+1}{4}-2=\frac{x+1}{3}\] Q.3 \[9-\frac{1}{2}x=5(x+4)\]

Follow my guides to solve the following confusing word problems with the best explanations.

Q.1

The mean age of 6 children is 12 years. When the age of seventh child is added, the mean reduces to 11 years. What is the age of the seventh child?

Q.2 Find three consecutive odd integers such that the sum of the last twi is 15 less than 5 times the first.

The answers will be provided later after you have tried them