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Solve for
x.

4x-39 > -43quad AND
quad8x+31 < 23
Choose 1 answer:
(A)
x < -1 or
x > -1
(B)
x < -1
(C)
x > -1
(D) There are no solutions
(E) All values of
x are solutions

Solve for $x$ . $\newline$ $4 x-39>-43 \quad$ AND $\quad 8 x+31<23$ $\newline$ Choose $1$ answer: $\newline$ (A) $x<-1$ or $x>-1$ $\newline$ (B) $x<-1$ $\newline$ (C) $x>-1$ $\newline$ (D) There are no solutions $\newline$ (E) All values of $x$ are solutions

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View step-by-step help

Solve a quadratic equation by factoring

Full solution

Q. Solve for

x

.

\newline

4 x-39>-43 \quad

AND

\quad 8 x+31<23

\newline

Choose

1

answer:

\newline

(A)

x<-1

or

x>-1

\newline

(B)

x<-1

\newline

(C)

x>-1

\newline

(D) There are no solutions

\newline

(E) All values of

x

are solutions

Solve first inequality: Solve the first inequality $4x - 39 > -43$ . $\newline$ Add $39$ to both sides to isolate the term with $x$ . $\newline$ $4x - 39 + 39 > -43 + 39$ $\newline$ $4x > -4$
Isolate $x$ term in first inequality: Divide both sides by $4$ to solve for $x$ .
$\frac{4x}{4} > \frac{-4}{4}$
$x > -1$
Solve second inequality: Solve the second inequality $8x + 31 < 23$ .
Subtract $31$ from both sides to isolate the term with $x$ .
$8x + 31 - 31 < 23 - 31$
$8x < -8$
Isolate $x$ term in second inequality: Divide both sides by $8$ to solve for $x$ .
$\frac{8x}{8} < \frac{-8}{8}$
$x < -1$
Combine solutions of both inequalities: Combine the solutions of both inequalities to find the common solution set. $\newline$ The first inequality gives us $x > -1$ , and the second inequality gives us $x < -1$ . $\newline$ Since there is no overlap between $x > -1$ and $x < -1$ , there are no values of $x$ that satisfy both inequalities at the same time.

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