Question

4x/2+8/2​=3x−6

1 point

12. Solve the compound inequality: 

2<3x−4<11

1 point

13. Write the equation of the line through (–3, 4) with slope -1/2​.  

1 point

  14. Convert to slope-intercept form and identify slope & y-intercept:  

5x+3y=12

1 point

15. Solve the system: 

y=7−x 

2x+y=10

1 point

Answer 1

1) 4x/2 + 8/2 = 3x − 6
2x + 4 = 3x − 6
4 + 6 = x
x = 10

12) 2 < 3x − 4 < 11
Add 4: 6 < 3x < 15
Divide by 3: 2 < x < 5
Solution: 2 < x < 5

13) Line through (−3, 4) with slope −1/2
Point-slope: y − 4 = −1/2(x + 3)
Slope-intercept: y = −1/2 x + 5/2
Slope = −1/2, y-intercept = 5/2

14) 5x + 3y = 12
3y = −5x + 12 → y = −5/3 x + 4
Slope = −5/3, y-intercept = 4

15) y = 7 − x
2x + y = 10
Substitute: 2x + (7 − x) = 10 → x + 7 = 10 → x = 3
y = 7 − 3 = 4
Solution: (x, y) = (3, 4)