Complete the tables for the equations y = x + 3 and 2x + y = 6, and solve the inequality 7x − 3 14.

Question

Complete the tables for the equations y = x + 3 and 2x + y = 6, and solve the inequality 7x − 3 > 14.

ScanSolve AI Tutor · Accepted Answer

a) To complete the table for the equation $y = x + 3$ :

Find $y$ when $x = -2$ .
$y = -2 + 3 = 1$
Find $x$ when $y = 7$ .
$7 = x + 3$ $x = 7 - 3 = 4$
Find $y$ when $x = 0$ .
$y = 0 + 3 = 3$
Find $y$ when $x = 2$ .
$y = 2 + 3 = 5$
Find $x$ when $y = 7$ (for the last column).
$7 = x + 3$ $x = 7 - 3 = 4$
The completed table is:

x -2 4 0 2 4
y 1 7 3 5 7

b) To complete the table for the equation $2x + y = 6$ :
Find $y$ when $x = 4 \frac{1}{2} = \frac{9}{2}$ .
$2\left(\frac{9}{2}\right) + y = 6$ $9 + y = 6$ $y = 6 - 9 = -3$
Find $x$ when $y = -2$ .
$2x + (-2) = 6$ $2x - 2 = 6$ $2x = 6 + 2$ $2x = 8$ $x = \frac{8}{2} = 4$
Find $x$ when $y = 0$ .
$2x + 0 = 6$ $2x = 6$ $x = \frac{6}{2} = 3$
Find $y$ when $x = 5$ .
$2(5) + y = 6$ $10 + y = 6$ $y = 6 - 10 = -4$
Find $y$ when $x = 3$ .
$2(3) + y = 6$ $6 + y = 6$ $y = 6 - 6 = 0$
The completed table is:

x $4 \frac{1}{2}$ 4 3 5 3
y -3 -2 0 -4 0
1. Solve the following inequalities
a) $7x - 3 > 14$
Add 3 to both sides of the inequality.
$7x - 3 + 3 > 14 + 3$ $7x > 17$
Divide both sides by 7.
$\frac{7x}{7} > \frac{17}{7}$ $x > \frac{17}{7}$
The solution is $\boxed{x > \frac{17}{7}}$ .

Point	x	y
x-intercept	−3	0
y-intercept	0	3

Complete the tables for the equations y = x + 3 and 2x + y = 6, and solve the inequality 7x − 3 > 14.