The image contains several math problems involving solving for variables and finding the area of parallelograms. We need to solve equations for $x$, and also find the area $y$ of a parallelogram with base 12cm and height $x$, given a height of 5cm. We also need to find the height $x$ of a parallelogram with base 12cm and area 90cm$^2$.

1. Problem Description

The image contains several math problems involving solving for variables and finding the area of parallelograms. We need to solve equations for $x$, and also find the area $y$ of a parallelogram with base 12cm and height $x$, given a height of 5cm. We also need to find the height $x$ of a parallelogram with base 12cm and area 90cm$^2$.

2. Solution Steps

Problem 1:

$x + 6 = 31$

Subtract 6 from both sides:

$x = 31 - 6$

$x = 25$

Problem 2:

$2x - 42 = 20$

Add 42 to both sides:

$2x = 20 + 42$

$2x = 62$

Divide both sides by 2:

$x = 62 / 2$

$x = 31$

Problem 3:

$x \times 7 = 56$

Divide both sides by 7:

$x = 56 / 7$

$x = 8$

Problem 4:

$x \div 5 = 9$

Multiply both sides by 5:

$x = 9 \times 5$

$x = 45$

Problem 5:

Area of a parallelogram = base * height

Given base = 12 cm and height = $x$ cm, the area $y$ is:

$y = 12 \times x$

Problem 6:

Given height = 5 cm, base = 12 cm, area = $y$ cm$^2$

$y = 12 \times 5$

$y = 60$

Problem 7:

Given area = 90 cm$^2$, base = 12 cm, height = $x$ cm

Area = base * height

$90 = 12 \times x$

Divide both sides by 12:

$x = 90 / 12$

$x = 7.5$

3. Final Answer

1. $x = 25$

2. $x = 31$

3. $x = 8$

4. $x = 45$

5. $y = 12x$

6. $y = 60$

7. $x = 7.5$