Chapter 2: Q. 64 (page 112)

In the following exercises, solve each equation with fraction coefficients.
$\frac{3 v - 6}{2} + 5 = \frac{11 v - 4}{5}$

Short Answer

Expert verified

The value of $v = 4$

Step by step solution

Step 1. Given Information

In the given question we have to solve equation with fraction coefficients.

$\frac{3 v - 6}{2} + 5 = \frac{11 v - 4}{5}$

Step 2. The given equation is 3v−62+5=11v−45

Now we solve the given equation for the value of $v$

Step 3. We want to clear the fractions by multiplying both sides of the equation by the LCD of all the fractions in the equation.

Finding the LCD of all fractions in the equation.

The numbers are $2, 5$

So the LCD is $10$

Step 4. Multiply both sides of the equation by 10.

$10 (\frac{3 v - 6}{2} + 5) = 10 (\frac{11 v - 4}{5})$

Distribute.

role="math" localid="1645456240112" $10 \times \frac{3 v - 6}{2} + 10 \times 5 = 5 (11 v - 4) 5 (3 v - 6) + 50 = 2 (11 v - 4) 15 v - 30 + 50 = 22 v - 8 15 v + 20 = 22 v - 8$

Step 5. Simplify—notice, no more fractions.

Subtract on both side

$15 v + 20 - 15 v = 22 v - 8 - 15 v 7 v - 8 = 20$

Add 8 on both side

$7 v - 8 + 8 = 20 + 8 7 v = 28 \frac{7}{7} v = \frac{28}{7} v = 4$

Step 6. Now checking the value.

Putting $v = 4$ in the given equation

role="math" localid="1645456429363" $\frac{3 \times 4 - 6}{2} + 5 = \frac{11 \times 4 - 4}{5} \frac{12 - 6}{2} + 5 = \frac{44 - 4}{5} \frac{6}{2} + 5 = \frac{40}{5} 3 + 5 = 8 8 = 8$

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In the following exercises, solve each equation with fraction coefficients.
$\frac{3 v - 6}{2} + 5 = \frac{11 v - 4}{5}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. The given equation is 3v−62+5=11v−45

Step 3. We want to clear the fractions by multiplying both sides of the equation by the LCD of all the fractions in the equation.

Step 4. Multiply both sides of the equation by 10.

Step 5. Simplify—notice, no more fractions.

Step 6. Now checking the value.

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In the following exercises, solve each equation with fraction coefficients. 3v−62+5=11v−45

Short Answer

Step by step solution

Step 1. Given Information

Step 2. The given equation is 3v−62+5=11v−45

Step 3. We want to clear the fractions by multiplying both sides of the equation by the LCD of all the fractions in the equation.

Step 4. Multiply both sides of the equation by 10.

Step 5. Simplify—notice, no more fractions.

Step 6. Now checking the value.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Geometry

Pure Maths

Applied Mathematics

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each equation with fraction coefficients.
$\frac{3 v - 6}{2} + 5 = \frac{11 v - 4}{5}$