# ACT Math : Equations / Inequalities

## Example Questions

### Example Question #31 : Linear / Rational / Variable Equations

What is the slope of the line 7y – 4x = 27

Explanation:

Adding 4x to both sides of the equation and dividing by 7 yields a slope of 4/7.

### Example Question #31 : Linear / Rational / Variable Equations

If you drove at an average speed of 78 miles per hour, what distance, in miles, did you drive in 140 minutes?

156

4,680

1.8

182

182

Explanation:

140 minutes is 7/3 of an hour. Multiplied by the speed of 78mph, we obtain 182 miles traveled.

### Example Question #32 : Linear / Rational / Variable Equations

3x + 9i2 – 5x = 17

What is x?

–4

–13

4

–1

13

–13

Explanation:

i =

i2 = -1

3x + 9i2 – 5x = 17

3x + 9(–1) – 5x = 17

–2x – 9 = 17

–2x = 26

x = –13

### Example Question #1801 : Act Math

Solve for x:

3x + 4y = 26

–5x + 12y = 14

Explanation:

Eliminate y and solve for x.

3x + 4y = 26 (multiply by –3)

–5x + 12y = 14

(–3)3x +(–3) 4y = (–3)26

–5x + 12y = 14

–9x +-12y = –78

–5x + 12y = 14

–14x + 0y = –64

x = –64/–14 = 32/7

.

### Example Question #134 : Algebra

John goes on a trip of  kilometers at a speed of  kilometers an hour. How long did the trip take?

Explanation:

If we take the units and look at division,  will yield hours as a unit. Therefore the answer is .

### Example Question #135 : Algebra

With a  head wind a plane can fly a certain distance in five hours.  The return flight takes an hour less.  How fast was the plane flying?