Question

variables and expressions
an expression that contains a combination of variables, numbers, and at least one operation is called an algebraic expression. a variable is any symbol, such as x, y, or a, that may be replaced with numbers. an algebraic expression can be evaluated by simply replacing the variables in the expression with their assigned values and then finding the numerical value of the expression.
evaluate each expression if x = 2 and y = 5.

1. 6x - 2y

6(2)-2(5)
12 - 10
2

1. 4x+(5 + 3y)-13

4(2)+(5 + 3(5))-13
8+(5 + 15)-13
8 + 20 - 13
28 - 13
15
evaluate each expression given the value of its variable.

1. y + 2; y = 4
2. \\(\frac{6a}{3}\\); a = 3
3. \\(\frac{10d}{4}-8\\); d = 6
4. x - 7; x = 12
5. 2c - 4; c = 5
6. 12 - 5z; z = 2

Explanation:

Step1: Substitute value for y

For the expression $y + 2$ with $y = 4$, we substitute $y$: $4+2$.

Step2: Calculate result

$4 + 2=6$.

Step3: Substitute value for a

For the expression $\frac{6a}{3}$ with $a = 3$, we substitute $a$: $\frac{6\times3}{3}$.

Step4: Calculate result

$\frac{18}{3}=6$.

Step5: Substitute value for d

For the expression $\frac{10d}{4}-8$ with $d = 6$, we substitute $d$: $\frac{10\times6}{4}-8$.

Step6: Calculate fraction part

$\frac{60}{4}=15$.

Step7: Calculate final result

$15 - 8=7$.

Step8: Substitute value for x

For the expression $x - 7$ with $x = 12$, we substitute $x$: $12-7$.

Step9: Calculate result

$12 - 7 = 5$.

Step10: Substitute value for c

For the expression $2c-4$ with $c = 5$, we substitute $c$: $2\times5-4$.

Step11: Calculate multiplication part

$2\times5 = 10$.

Step12: Calculate final result

$10-4=6$.

Step13: Substitute value for z

For the expression $12-5z$ with $z = 2$, we substitute $z$: $12-5\times2$.

Step14: Calculate multiplication part

$5\times2 = 10$.

Step15: Calculate final result

$12-10 = 2$.

Answer:

1. 6
2. 6
3. 7
4. 5
5. 6
6. 2