Q25. - Algebra 1

Question

Solve each equation.

$(4-2^2+5)w=25$

Step-by-Step Solution

Answer

The value of $\mathit{w}$ is 5

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

Addition Property of Equality

If any two expressions are equal to each other, If we add the same value to both sides of the equation, the equation will remain equal.

For all real numbers a, b, and c: If a = b, then a + c = b + c.

Since subtraction can be written as an addition (adding the opposite), the addition property of equality can be used for subtraction as well.

Multiplication Property of Equality

If two expressions are equal to each other and you multiply both sides by the same number, the resulting expressions will also be equivalent.

For all real numbers a, b, and c: If a = b, then a • c = b • c or (ab = ac).

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. Apply BODMAS Rule.

$(4-2^2+5)w=25$ Original equation

First, we do operations in brackets.

Evaluate powers in the bracket.

$\Rightarrow (4-4+5)w=25$

Add the numbers 5 and 4.

$\Rightarrow (9-4)w=25$

Subtracting 4 from 9.

$\Rightarrow \left(5\right)w=25$

Divide both sides by 5 using the multiplication property of equality

$\Rightarrow w=5$

Thus, the value of w is 5.