Q24. - Algebra 1

Question

Solve each equation.

$\mathit{a}\mathbf{=}\frac{\mathbf{4}\mathbf{(}\mathbf{14}\mathbf{-}\mathbf{1}\mathbf{)}}{\mathbf{3}\mathbf{\left(}\mathbf{6}\mathbf{\right)}\mathbf{-}\mathbf{5}}\mathbf{+}\mathbf{7}$

Step-by-Step Solution

Answer

The value of a is 11.

Step 1. Definition.

Equation: An equation is a mathematical statement that two expressions are equal. An equation will always contain an equal sign with an expression on each side.

Step 2. Order of Operations.

BODMAS

B – Brackets First

O – Orders (i.e. Powers and Square Roots etc.)

D – Division

M – Multiplication

A – Addition

S – Subtraction

Step 3. Simplifying ratio.

$a=\frac{4(14-1)}{3\left(6\right)-5}+7$ Original equation

First, we work on the numerator, subtracting 1 from 14.

$\Rightarrow a=\frac{4\left(13\right)}{3\left(6\right)-5}+7$

In the denominator, multiply 6 by 3.

$\Rightarrow a=\frac{4\left(13\right)}{18-5}+7$

In the denominator, Subtract 5 from 18.

$\Rightarrow a=\frac{4\left(13\right)}{13}+7$

Divide by 13 in the first term of the equation on the Right-hand side of the equation.

$\Rightarrow a=4+7$

Add 4 and 7, we get

$\Rightarrow a=11$

Therefore, the value of a is 11.