STAAR Algebra I Number and Algebraic Methods. Practice it free.

The equation means $x - 14 = 20$ or $x - 14 = -20$. So $x = 34$ or $x = -6$. Both solutions are $-6$ and $34\textsf{.}$

Rewrite $|4x + 16| = |4(x + 4)| = |4|\,|x + 4| = 4|x + 4|$. Since $4|x + 4| = 52$, divide by $4$ to get $|x + 4| = 13$. The expression $x + 4$ equals $13$ or $-13$; the negative value is $-13\textsf{.}$

The greatest common factor of $10x^{2}$ and $15x$ is $5x\textsf{.}$ Factoring gives $5x(2x - 3)$.

$16x^{2} - 49 = (4x)^{2} - 7^{2} = (4x - 7)(4x + 7)$.

Write $36m$ with denominator $t$: $\dfrac{18m}{t} + \dfrac{36mt}{t} = \dfrac{18m + 36mt}{t} = \dfrac{18m(1 + 2t)}{t}$.

Half of $10$ is $5$ and $5^{2} = 25$, so $x^{2} + 10x + 25 = (x + 5)^{2}$ and $a = 5$.

Two numbers that multiply to $12$ and add to $7$ are $3$ and $4$. So $x^{2} + 7x + 12 = (x + 3)(x + 4)$.

Add $15$ to both sides: $3x = 15$, so $x = 5$. Then $x + 4 = 5 + 4 = 9\textsf{.}$