Question

1. solve the equation:

2(9x - 6) = 6(3x - 2) + 2

1. solve the equation:

8 + 4x = 2x + 8 + 2x
i can write and solve an equation from a verbal description.

1. write and solve an equation for the

following situation:
marshall earns a salary of $36,000, and each
year he receives a $4,000 raise. jim earns a
salary of $51,000, and each year he receives a
$1,500 raise. how many years will it take
before marshall and jim earn the same salary?
equation:
x:

1. the square and equilateral triangle below

have the same perimeter. find the value of x.
then, find the perimeter of each shape.
equation:
x:
perimeter:

1. write and solve an equation based on the

following description:
\46 less than -8 times a number is the same as
8 less than -6 times the number\
equation:
solution:

1. write and solve an equation based on the

following description:
\a number increased by 11 is equal to twice the
number decreased by 12\
equation:
solution:
i can solve one and two-step linear inequalities.

1. solve the inequality and graph the solution.

\\( \frac { 7 } { 2 } w > - 14 \\)

1. solve the inequality and graph the solution.

\\( - 8 x + 15 \geq - 26.6 \\)

Explanation:

20.

Step1: Set up the equation

Let \(x\) be the number of years. Marshall's salary is \(36000 + 4000x\), and Jim's salary is \(51000+1500x\). The equation is \(36000 + 4000x=51000 + 1500x\).

Step2: Solve the equation

Subtract \(1500x\) from both sides: \(36000+4000x - 1500x=51000+1500x-1500x\), which simplifies to \(36000 + 2500x=51000\).
Subtract \(36000\) from both sides: \(2500x=51000 - 36000\), so \(2500x = 15000\).
Divide both sides by \(2500\): \(x=\frac{15000}{2500}=6\).

21.

Step1: Set up the equation

The perimeter of the square is \(4(2x + 5)\), and the perimeter of the equilateral triangle is \(3(2x + 8)\). The equation is \(4(2x + 5)=3(2x + 8)\).

Step2: Expand the equation

\(8x+20 = 6x+24\).

Step3: Solve the equation

Subtract \(6x\) from both sides: \(8x - 6x+20=6x - 6x+24\), so \(2x+20 = 24\).
Subtract \(20\) from both sides: \(2x=24 - 20\), so \(2x = 4\).
Divide by \(2\): \(x = 2\).

Step4: Find the perimeter

Substitute \(x = 2\) into the square's perimeter formula: \(4(2\times2 + 5)=4(4 + 5)=36\).

22.

Step1: Translate the description to an equation

Let the number be \(x\). The equation is \(-8x-46=-6x - 8\).

Step2: Solve the equation

Add \(8x\) to both sides: \(-46=-6x+8x - 8\), so \(-46 = 2x-8\).
Add \(8\) to both sides: \(2x=-46 + 8=-38\).
Divide by \(2\): \(x=-19\).

23.

Step1: Translate the description to an equation

Let the number be \(x\). The equation is \(x + 11=2x-12\).

Step2: Solve the equation

Subtract \(x\) from both sides: \(11=2x-x-12\), so \(x=11 + 12=23\).

24.

Step1: Solve the inequality \(\frac{7}{2}w>-14\)

Multiply both sides by \(\frac{2}{7}\): \(w>-14\times\frac{2}{7}\), so \(w>-4\).

25.

Step1: Solve the inequality \(-8x + 15\geq-26.6\)

Subtract \(15\) from both sides: \(-8x\geq-26.6-15\), so \(-8x\geq-41.6\).
Divide both sides by \(-8\) (and reverse the inequality sign): \(x\leq\frac{-41.6}{-8}=5.2\).

Answer:

1. Equation: \(36000 + 4000x=51000 + 1500x\), \(x = 6\)
2. Equation: \(4(2x + 5)=3(2x + 8)\), \(x = 2\), Perimeter: \(36\)
3. Equation: \(-8x-46=-6x - 8\), Solution: \(x=-19\)
4. Equation: \(x + 11=2x-12\), Solution: \(x = 23\)
5. Solution: \(w>-4\)
6. Solution: \(x\leq5.2\)