Question

1. which of the following equations does not have x=8 as a solution?

(1) \\(\frac{x}{2}=4\\) (3) 3x=18
(2) x - 3 = 5 (4) x + 7 = 15
using your math

1. a rectangle had a length of 12 feet, an area of 60 square feet, and an unknown width. let w be the width of the rectangle.

set up an equation involving w and solve it for the width of the rectangle.
(image of a rectangle with length 12 ft, width w, and area = 60 square feet)

1. sonia is sorting her rock collection into jars that each hold five rocks. she fills a total of eight jars. let r be the total number of rocks sonia has. write an equation involving r and solve it for the total number of rocks sonia has.

reviewing your math

1. find the quotient in (a) and check it in (b) using multiplication.

(a) \\(6.3\overline{)17.64}\\) (b) check with multiplication:

Explanation:

Problem 4

Step1: Test x=8 in Eq(1)

Substitute $x=8$ into $\frac{x}{2}=4$: $\frac{8}{2}=4$, $4=4$, valid.

Step2: Test x=8 in Eq(2)

Substitute $x=8$ into $x-3=5$: $8-3=5$, $5=5$, valid.

Step3: Test x=8 in Eq(3)

Substitute $x=8$ into $3x=18$: $3\times8=24
eq18$, invalid.

Step4: Test x=8 in Eq(4)

Substitute $x=8$ into $x+7=15$: $8+7=15$, $15=15$, valid.

Problem 5

Step1: Set area equation

Area of rectangle: $12w=60$

Step2: Solve for w

Divide both sides by 12: $w=\frac{60}{12}=5$

Problem 6

Step1: Set total rocks equation

Total rocks: $\frac{r}{5}=8$

Step2: Solve for r

Multiply both sides by 5: $r=8\times5=40$

Problem 7

Step1: Compute the quotient

Convert decimals to integers: $\frac{17.64}{6.3}=\frac{176.4}{63}=2.8$

Step2: Verify with multiplication

Multiply quotient and divisor: $2.8\times6.3=17.64$

Answer:

1. (3) $3x=18$
2. The width of the rectangle is 5 feet.
3. Sonia has 40 rocks.
4. (a) The quotient is $2.8$; (b) $2.8\times6.3=17.64$, which matches the dividend, so the quotient is correct.