Question

1. write an expression and evaluate for the following scenario.

c. carlos makes $12 per hour washing cars and averages a $5 tip per car he washes. let h = hours, and t = tip.
d. how much should carlos make if he washes 6 cars in 4 hours?

1. solve for a in the following equation y = ab + c
2. solve and graph the solution for: - 1 + x < 4 and 2x + 5 > - 9.
3. solve and graph the solution for: - 4x < 24 or 3x + 5 < - 19.

fill in the blank using the vocabulary words from the word bank.
absolute - value coefficient constant equation evaluate expression
like terms opposite reciprocal solution term variable

1. in algebra, a is a number, variable, or a product of both, separated by addition or subtraction in an expression.
2. an is a mathematical statement that shows two expressions are equal, usually with an \=\ sign.
3. 2x and 3x are examples of because they have the same variable raised to the same power.
4. an is a mathematical phrase that combines numbers, variables, and operations but does not include an equal sign.
5. in the term 7y, the number 7 is called a.
6. in the expression 3x + 5, the number 5 is called a because its value does not change.
7. to an expression means to find its value by substituting numbers for variables.
8. the of an equation is the value that makes the equation true.

Explanation:

7c.

Step1: Determine the income from hourly - work

The income from hourly - work is the product of the hourly rate and the number of hours. Carlos makes $12 per hour, and the number of hours is $h$. So the income from hourly - work is $12h$.

Step2: Determine the income from tips

Carlos gets a $5 tip per car, and if the number of cars is $n$, the income from tips is $5n$.

Step3: Write the total income expression

Let the total income be $I$. Then $I = 12h+5n$.

7d.

Step1: Identify the values of $h$ and $n$

Given that $h = 4$ (number of hours) and $n = 6$ (number of cars).

Step2: Substitute the values into the expression

Substitute $h = 4$ and $n = 6$ into the expression $I = 12h + 5n$.
$I=12\times4+5\times6$.

Step3: Calculate the result

First, calculate $12\times4 = 48$ and $5\times6=30$.
Then $I=48 + 30=78$.

Step1: Isolate the term with $a$

Given the equation $y=ab + c$. Subtract $c$ from both sides of the equation to get $y - c=ab$.

Step2: Solve for $a$

Divide both sides of the equation $y - c=ab$ by $b$ (assuming $b
eq0$). So $a=\frac{y - c}{b}$.

Answer:

Carlos should make $78$.

8.