Question

question 6 (1 point)
solve the inequality.
$x + 4 \leq -16$
\\(\circ\\) a \\(x \leq -20\\)
\\(\circ\\) b \\(x \leq -12\\)
\\(\circ\\) c \\(x \geq -20\\)

question 7 (1 point)
solve the inequality.
$m - 10 > -35$
\\(\circ\\) a \\(m < -25\\)
\\(\circ\\) b \\(m > 45\\)
\\(\circ\\) c \\(m > -25\\)

Explanation:

Question 6

Step1: Subtract 4 from both sides

To solve the inequality \( x + 4 \leq -16 \), we subtract 4 from both sides of the inequality. This is done to isolate the variable \( x \). The operation of subtracting 4 from both sides is valid because subtracting the same number from both sides of an inequality does not change the direction of the inequality sign.
\[
x + 4 - 4 \leq -16 - 4
\]

Step2: Simplify both sides

Simplifying the left - hand side, \( x+4 - 4=x \). Simplifying the right - hand side, \( - 16-4=-20 \). So we get:
\[
x\leq - 20
\]

Step1: Add 10 to both sides

To solve the inequality \( m - 10>-35 \), we add 10 to both sides of the inequality. Adding the same number to both sides of an inequality does not change the direction of the inequality sign. This step is used to isolate the variable \( m \).
\[
m-10 + 10>-35 + 10
\]

Step2: Simplify both sides

Simplifying the left - hand side, \( m - 10+10=m \). Simplifying the right - hand side, \( -35 + 10=-25 \). So we get:
\[
m>-25
\]
(Note: There seems to be a typo in the given options for Question 7 as the correct answer \( m > - 25\) is not among the provided options. If we assume a possible typo and the intended option for \(m>-25\) was miswritten, but based on the calculation, the solution to \(m - 10>-35\) is \(m>-25\))

Answer:

a. \( x\leq - 20 \)

Question 7