Question

Which values from the set {−6, −4, −3, −1, 0, 2} satisfy this inequality?
−1/2x + 3 ≥ 5

Answer 1

Answer:

The values  $x=-6$ and $x=-4$ satisfy this inequality

Step-by-step explanation:

Let us look at each individual value of the set  {−6, −4, −3, −1, 0, 2} with regards to the inequality

$x=-6\\\\\frac{-1}{2}(-6)+3\geq 5\\3+3\geq 5\\\\6\geq 5$

As this inequality is true, $x=-6$ satisfies this inequality

$x=-4\\\\\frac{-1}{2}(-4)+3\geq 5\\\\2+3\geq 5\\\\5\geq 5$

As this inequality is true, $x=-4$ satisfies this inequality

$x=-3\\\\\frac{-1}{2}(-3)+3\geq 5\\\\\frac{3}{2} +3\geq 5\\\\\frac{9}{2} \geq 5$

As this inequality is false, $x=-3$ does not satisfy the inequality

$x=-1\\\\\frac{-1}{2}(-1)+3\geq 5\\\\\frac{1}{2} +3\geq 5\\\\\frac{7}{2} \geq 5$

As this inequality is false, $x=-1$ does not satisfy the inequality

$x=-0\\\\\frac{-1}{2}(0)+3\geq 5\\\\3\geq 5$

As this inequality is false, $x=0$ does not satisfy the inequality

$x=2\\\\\frac{-1}{2}(2)+3\geq 5\\\\-1+3\geq 5\\\\2\geq 5$

As this inequality is false, $x=2$ does not satisfy the inequality

Answer 2

The values from the set less than -4 is -6

Given the inequality expression

• −1/2x + 3 ≥ 5

Subtract 3 from both sides

−1/2x + 3 - 3 ≥ 5 - 3

-1/2x ≥ 5 - 3

-x ≥ 2 * 2

- x ≥ 4

x ≤  -4

This shows that the value of x must be less than -4. The values from the set less than -4 is -6

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