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Solve the following Linear Inequalities for
X. Then, Write your answer in BOTH inequality and interva notation.
5.
2x+4y < 8
6.
-3x-y >= 2
7.
x-(1)/(2)y > 5
Inequality:
qquad Inequality:
qquad Inequality:
qquad

4y < 2x+8

qquad

qquad
Interval:
qquad Interval:
qquad Interval:
qquad
8.
-2 < 3x+1 < 7
9.
2x <= -16 or
6x-1 >= 5
Inequality:
qquad Inequality:
qquad
Interval:
qquad Interval:
qquad

Solve the following Linear Inequalities for $\mathrm{X}$ . Then, Write your answer in BOTH inequality and interva notation. $\newline$ $5$ . $2 x+4 y<8$ $\newline$ $6$ . $-3 x-y \geq 2$ $\newline$ $7$ . $x-\frac{1}{2} y>5$ $\newline$ Inequality: $\qquad$ Inequality: $\qquad$ Inequality: $\qquad$ $\newline$ $4 y<2 x+8$ $\newline$ $\qquad$ $\newline$ $\qquad$ $\newline$ Interval: $\qquad$ Interval: $\qquad$ Interval: $\qquad$ $\newline$ $8$ . $2 x+4 y<8$ $3$ $\newline$ $9$ . $2 x+4 y<8$ $4$ or $2 x+4 y<8$ $5$ $\newline$ Inequality: $\qquad$ Inequality: $\qquad$ $\newline$ Interval: $\qquad$ Interval: $\qquad$

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One-step inequalities: word problems

Full solution

Q. Solve the following Linear Inequalities for

\mathrm{X}

. Then, Write your answer in BOTH inequality and interva notation.

\newline

5

.

2 x+4 y<8

\newline

6

.

-3 x-y \geq 2

\newline

7

.

x-\frac{1}{2} y>5

\newline

Inequality:

\qquad

Inequality:

\qquad

Inequality:

\qquad

\newline

4 y<2 x+8

\newline

\qquad

\newline

\qquad

\newline

Interval:

\qquad

Interval:

\qquad

Interval:

\qquad

\newline

8

.

2 x+4 y<8

3

\newline

9

.

2 x+4 y<8

4

or

2 x+4 y<8

5

\newline

Inequality:

\qquad

Inequality:

\qquad

\newline

Interval:

\qquad

Interval:

\qquad

Isolate $x$ : For $2x + 4y < 8$ , isolate $x$ by subtracting $4y$ from both sides. $\newline$ $2x < 8 - 4y$
Solve for x: Divide both sides by $2$ to solve for x. $x < 4 - 2y$ Inequality: $x < 4 - 2y$ Interval: $(-\infty, 4 - 2y)$
Add $y$ : For $-3x - y \geq 2$ , add $y$ to both sides. $\newline$ $-3x \geq 2 + y$
Divide by $-3$ : Divide both sides by $-3$ , remembering to flip the inequality sign because we're dividing by a negative number. $\newline$ $x \leq -(2 + y)/3$ $\newline$ Inequality: $x \leq -(2 + y)/3$ $\newline$ Interval: $(-\infty, -(2 + y)/3]$
Add $(\frac{1}{2})y$ : For $x - (\frac{1}{2})y > 5$ , add $(\frac{1}{2})y$ to both sides. $\newline$ $x > 5 + (\frac{1}{2})y$ $\newline$ Inequality: $x > 5 + (\frac{1}{2})y$ $\newline$ Interval: $(5 + (\frac{1}{2})y, \infty)$
Subtract $1$ : For $-2 < 3x + 1 < 7$ , subtract $1$ from all parts of the inequality. $\newline$ $-3 < 3x < 6$
Divide by $3$ : Divide all parts by $3$ . $\newline$ $-1 < x < 2$ $\newline$ Inequality: $-1 < x < 2$ $\newline$ Interval: $(-1, 2)$
Divide by $2$ : For $2x \leq -16$ , divide both sides by $2$ . $\newline$ $x \leq -8$ $\newline$ Inequality: $x \leq -8$ $\newline$ Interval: $(-\infty, -8]$
Add $1$ : For $6x - 1 \geq 5$ , add $1$ to both sides. $\newline$ $6x \geq 6$
Combine solutions: Divide both sides by $6$ . $\newline$ $x \geq 1$ $\newline$ Inequality: $x \geq 1$ $\newline$ Interval: $[1, \infty)$
Combine solutions: Divide both sides by $6$ . $\newline$ $x \geq 1$ $\newline$ Inequality: $x \geq 1$ $\newline$ Interval: $[1, \infty)$ Combine the solutions for the ＂or＂ inequality. $\newline$ $x \leq -8$ or $x \geq 1$ $\newline$ Inequality: $x \leq -8$ or $x \geq 1$ $\newline$ Interval: $(-\infty, -8] \cup [1, \infty)$

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