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Solve for
x.

7x+39 >= 53quad AND
quad16 x+15 > 31
Choose 1 answer:
(A)
x > 1
(B)
x >= 2
(C)
x <= 2
D There are no solutions
(E) All values of
x are solutions

Solve for $x$ . $\newline$ $7 x+39 \geq 53 \quad$ AND $\quad 16 x+15>31$ $\newline$ Choose $1$ answer: $\newline$ (A) $x>1$ $\newline$ (B) $x \geq 2$ $\newline$ (C) $x \leq 2$ $\newline$ D There are no solutions $\newline$ (E) All values of $x$ are solutions

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Solve a quadratic equation by factoring

Full solution

Q. Solve for

x

.

\newline

7 x+39 \geq 53 \quad

AND

\quad 16 x+15>31

\newline

Choose

1

answer:

\newline

(A)

x>1

\newline

(B)

x \geq 2

\newline

(C)

x \leq 2

\newline

D There are no solutions

\newline

(E) All values of

x

are solutions

Solve first inequality: Solve the first inequality $7x + 39 \geq 53$ . $\newline$ Subtract $39$ from both sides to isolate the term with $x$ . $\newline$ $7x + 39 - 39 \geq 53 - 39$ $\newline$ $7x \geq 14$
Isolate $x$ term: Divide both sides by $7$ to solve for $x$ . $\newline$ $\frac{$ $7$ x}{ $7$ } \geq \frac{ $14$ }{ $7$ } $\newline$ $x \geq$ $2$
Divide both sides: Solve the second inequality $16x + 15 > 31$ .
Subtract $15$ from both sides to isolate the term with $x$ .
$16x + 15 - 15 > 31 - 15$
$16x > 16$
Solve second inequality: Divide both sides by $16$ to solve for $x$ . $\newline$ $\frac{16x}{16} > \frac{16}{16}$ $\newline$ $x > 1$
Isolate x term: Combine the solutions of both inequalities to find the common solution set. $\newline$ From the first inequality, we have $x \geq 2$ . $\newline$ From the second inequality, we have $x > 1$ . $\newline$ The common solution set that satisfies both inequalities is $x \geq 2$ .

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