Question

ii. complete the table to check your prediction.

1. crisgo is solving the inequality ( 166 - 5x geq 56 ). first, he solves the equation ( 166 - 5x = 56 ) and gets ( x = 56 ). which inequality represents all the solutions for ( 166 - 5x geq 56 )?

a ( x < 56 )
c ( x > 56 )
b ( x leq 56 )
d ( x geq 56 )

1. solve the inequality ( 5(x - 6) < 45 ), and graph the solution on the number line.

Explanation:

Problem 2 (Multiple Choice)

Step1: Isolate the variable term

$100 - 2x \leq 50$
Subtract 100 from both sides:
$100 - 100 - 2x \leq 50 - 100$
$-2x \leq -50$

Step2: Solve for x, reverse inequality

Divide both sides by -2 (reverse inequality sign when dividing by negative number):
$\frac{-2x}{-2} \geq \frac{-50}{-2}$
$x \geq 50$

Step1: Isolate the parenthetical term

$5(x - 1) < 40$
Divide both sides by 5:
$\frac{5(x - 1)}{5} < \frac{40}{5}$
$x - 1 < 8$

Step2: Solve for x

Add 1 to both sides:
$x - 1 + 1 < 8 + 1$
$x < 9$

Step3: Graph explanation

On a number line, draw an open circle at 9 (since the inequality is strict, $x$ cannot equal 9) and shade all values to the left of 9.

Step1: Substitute each x into $y=100-2x$

For $x=-4$: $y=100-2(-4)=108$
For $x=-3$: $y=100-2(-3)=106$
For $x=-2$: $y=100-2(-2)=104$
For $x=-1$: $y=100-2(-1)=102$
For $x=0$: $y=100-2(0)=100$
For $x=1$: $y=100-2(1)=98$
For $x=2$: $y=100-2(2)=96$
For $x=3$: $y=100-2(3)=94$
For $x=4$: $y=100-2(4)=92$

Answer:

B. $x \geq 50$

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Problem 3