Question

7(2x - 3) = 63
which equation has the same solution as the given equation?
a) 2x - 3 = 9
b) 2x - 3 = 56
c) 2x - 21 = 63
d) 2x - 21 = 70

(x + 2)(x - 5)(x + 9) = 0
what is a positive solution to the given equation?
a) 3
b) 4
c) 5
d) 18

the function f defined by f(t) = 14t + 9 gives the estimated length, in inches, of a vine plant t months after trevon purchased it. which of the following is the best interpretation of 9 in this context?
a) trevon will keep the vine plant for 9 months.
b) the vine plant is expected to grow 9 inches each month.
c) the vine plant is expected to grow to a maximum length of 9 inches.
d) the estimated length of the vine plant was 9 inches when trevon purchased it.

brian saves \\( \frac { 2 } { 5 } \\) of the \\( \\$ 215 \\) he earns each week from his job. if brian continues to save at this rate, how much money, in dollars, will brian save in 9 weeks?

a rectangle has an area of 155 square inches. the length of the rectangle is 4 inches less than 7 times the width of the rectangle. what is the width of the rectangle, in inches?

Explanation:

First problem: \(7(2x - 3)=63\)

Step1: Divide both sides by 7

$$\frac{7(2x - 3)}{7}=\frac{63}{7}$$
$$2x - 3 = 9$$

Step1: Use zero - product property

If \(A\times B\times C = 0\), then \(A = 0\) or \(B=0\) or \(C = 0\).
Set \(x+2=0\), then \(x=-2\); set \(x - 5=0\), then \(x = 5\); set \(x+9=0\), then \(x=-9\)

Step1: Analyze the linear function

In the linear function \(y=mx + b\) (here \(y = f(t)\), \(m = 14\), \(b = 9\)), when \(t = 0\) (at the time of purchase), \(f(0)=14\times0+9=9\)

Answer:

A. \(2x - 3=9\)

Second problem: \((x + 2)(x - 5)(x + 9)=0\)