Question

22 what is the solution for the equation x + 1 = x + 2? 1) -1 2) $\frac{1}{2}$ 3) all real numbers 4) there is no solution. 23 debbie solved the linear equation 3(x + 4) - 2 = 16 as follows: line 1 3(x + 4) - 2 = 16 line 2 3(x + 4) = 18 line 3 3x + 4 = 18 line 4 3x = 14 line 5 x = 4$\frac{2}{3}$ she made an error between lines 1) 1 and 2 2) 2 and 3 3) 3 and 4 4) 4 and 5 24 solve for g: 3 + 2g = 5g - 9 25 solve for x: 5(x - 2) = 2(10 + x) 26 solve algebraically for x

Explanation:

Question 22

Step1: Try to solve the equation

Subtract \(x\) from both sides of \(x + 1=x + 2\). We get \(x - x+1=x - x + 2\), which simplifies to \(1 = 2\). This is a contradiction.

Step1: Analyze the steps of solving the equation \(3(x + 4)-2 = 16\)

In line 2, we add 2 to both sides of the equation correctly to get \(3(x + 4)=18\). In line 3, the error occurs. When distributing the 3 in \(3(x + 4)\), it should be \(3x+12\) not \(3x + 4\).

Step1: Isolate the variable terms

Subtract \(2g\) from both sides of \(3 + 2g=5g - 9\), we get \(3=5g-2g - 9\), which simplifies to \(3 = 3g-9\).

Step2: Further isolate the variable

Add 9 to both sides: \(3 + 9=3g\), so \(12 = 3g\).

Step3: Solve for \(g\)

Divide both sides by 3: \(g=\frac{12}{3}=4\)

Answer:

1. There is no solution

Question 23