Question

1. solve for ( x ) when ( y = 4 ) in the equation ( 3x + 6y = 18 ).

( circ ) a. ( -2 )
( circ ) b. ( 6 )
( circ ) c. ( 3 )
( circ ) d. ( 9 )

1. what is the first operation to perform when solving ( \frac{m + n}{o} = p ) for ( m )?

( circ ) a. multiply both sides by ( o )
( circ ) b. add ( n ) to both sides
( circ ) c. divide both sides by ( p )
( circ ) d. subtract ( n ) from both sides

1. to advance to the next round in a competition, contestants must score higher than 75 points. which inequality represents this scenario?

( circ ) a. ( x < 75 )
( circ ) b. ( x geq 75 )
( circ ) c. ( x > 75 )
( circ ) d. ( x leq 75 )

Explanation:

Question 17:

Step1: Substitute $y=4$

$3x + 6(4) = 18$

Step2: Simplify the constant term

$3x + 24 = 18$

Step3: Isolate the $x$-term

$3x = 18 - 24$
$3x = -6$

Step4: Solve for $x$

$x = \frac{-6}{3} = -2$

Question 18:

Step1: Identify the goal: isolate $m$

The equation is $\frac{m+n}{o}=p$. To free $m+n$ from the denominator, multiply both sides by $o$ first:
$m+n = p \cdot o$
This is the first necessary operation to start isolating $m$.

Question 19:

Step1: Translate "higher than 75"

Let $x$ = contestant's score. "Higher than 75" means the score must be strictly greater than 75, so the inequality is $x > 75$.

Answer:

1. a. $-2$
2. a. Multiply both sides by $o$
3. c. $x > 75$