Question

test prep

1. what missing value would make the equation have infinitely

solutions?
2(3 + 4x) = 8x +
a 1.5
b 3
6
d 6x

1. how many solutions does the following equation have? if there is only

one solution, find it.
3 + \\( \frac { 4 } { 5 } x = \frac { 9 } { 10 } x \\)

1. complete the equation so that it has no solution.

10.5x - 4 = 5 +

1. complete the equation so that it has the solution c = 4.

5(2c - ) = 2(c + 11)

1. how many solutions does the following equation have? if there is only

one solution, find it.
2x + 8 = 2(x + 3)
a one solution; x = -5
no solution
b one solution; x = 5
d infinitely many solutions
spiral review

1. complete each figure so it is congruent to the figure shown.
2. the coordinates of the vertices of the preimage of a triangle are

(2, 1), (3, 4), and (4, 1). the coordinates of the vertices of the image
are (3, 3), (4, 5), and (5, 3). how far and in what direction was the
triangle translated?

Explanation:

Step1: Simplify the left - hand side of the equation

Use the distributive property \(a(b + c)=ab+ac\). For \(2(3 + 4x)\), we have \(2\times3+2\times4x=6 + 8x\).
The equation becomes \(6 + 8x=8x+\square\).

Step2: Analyze the condition for infinitely many solutions

For an equation \(ax + b=ax + c\) to have infinitely many solutions, \(b = c\).
Since the left - hand side is \(8x + 6\) and the right - hand side is \(8x+\square\), when \(\square = 6\), the equation \(8x + 6=8x + 6\) is True for all \(x\) (because subtracting \(8x\) from both sides gives \(6 = 6\)).

Answer:

C. 6