(4p+3)/8 =(p+2)/4 — step-by-step solution

1) Let's solve in

ℝ

\frac{4 p + 3}{8} = \frac{p + 2}{4}

2) Let's sum the fractions:

\frac{4 p + 3}{8} - \frac{p + 2}{4} = 0

ⓘ To add fractions, put them over the same denominator, then add the numerators:

\frac{4 p + 3}{8} - \frac{p + 2}{4}

\frac{(4 p + 3) - (p + 2) \cdot 2}{8}

\frac{(4 p + 3) - (p + 2) \cdot 2}{8} = 0

\frac{4 p + 3 - (p + 2) \cdot 2}{8} = 0

Let's solve in

ℝ

4 p + 3 - (p + 2) \cdot 2 = 0

ⓘ Expand by multiplying each term inside the parentheses:

- (p + 2) \cdot 2

- (p \cdot 2 + 4)

4 p + 3 - (p \cdot 2 + 4) = 0

ⓘ A minus sign before a parenthesis changes the sign of each of its terms:

- (p \cdot 2 + 4)

- p \cdot 2 - 4

4 p

+ 3

- p \cdot 2

- 4 = 0

ⓘ Start from

3

and move back

4

on the number line, going below zero:

3 - 4

-1

■Like terms are grouped by adding their coefficients:

4 p - p \cdot 2

2 p

2 p - 1 = 0

2 p = 1

ⓘ Both sides are divided by

2

▶Solution found:

p = \frac{1}{2}

3) The numeric value of:

p = \frac{1}{2}

is:

▷

p = 0.5