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$^2$.

AlgebraLinear EquationsSolving for VariablesArea of ParallelogramGeometry
2025/7/3

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 xx, and also find the area yy of a parallelogram with base 12cm and height xx, given a height of 5cm. We also need to find the height xx of a parallelogram with base 12cm and area 90cm2^2.

2. Solution Steps

Problem 1:
x+6=31x + 6 = 31
Subtract 6 from both sides:
x=316x = 31 - 6
x=25x = 25
Problem 2:
2x42=202x - 42 = 20
Add 42 to both sides:
2x=20+422x = 20 + 42
2x=622x = 62
Divide both sides by 2:
x=62/2x = 62 / 2
x=31x = 31
Problem 3:
x×7=56x \times 7 = 56
Divide both sides by 7:
x=56/7x = 56 / 7
x=8x = 8
Problem 4:
x÷5=9x \div 5 = 9
Multiply both sides by 5:
x=9×5x = 9 \times 5
x=45x = 45
Problem 5:
Area of a parallelogram = base * height
Given base = 12 cm and height = xx cm, the area yy is:
y=12×xy = 12 \times x
Problem 6:
Given height = 5 cm, base = 12 cm, area = yy cm2^2
y=12×5y = 12 \times 5
y=60y = 60
Problem 7:
Given area = 90 cm2^2, base = 12 cm, height = xx cm
Area = base * height
90=12×x90 = 12 \times x
Divide both sides by 12:
x=90/12x = 90 / 12
x=7.5x = 7.5

3. Final Answer

1. $x = 25$

2. $x = 31$

3. $x = 8$

4. $x = 45$

5. $y = 12x$

6. $y = 60$

7. $x = 7.5$