Solving First-Degree Equations Practice Problems - All Methods

First we will move terms so that -b remains remains on the left side of the equation.

We'll move 8 to the right-hand side, making sure to retain the plus and minus signs accordingly:

$-b=6-8$

Then we will subtract as follows:

$-b=-2$

Finally, we will divide both sides by -1 (be careful with the plus and minus signs when dividing by a negative):

$\frac{-b}{-1}=\frac{-2}{-1}$

$b=2$

Let's solve the equation $-16 + a = -17$ by isolating the variable $a$.

To isolate $a$, add 16 to both sides of the equation to cancel out the $-16$:

$-16 + a + 16 = -17 + 16$

This simplification results in:

$a = -1$

Thus, the solution to the equation $-16 + a = -17$ is $a = -1$.

If we review the answer choices given, the correct answer is Choice 4, $-1$.

The solution to the problem is $a = -1$.

Step-by-step solution:

1. Begin with the equation: $x + 9 = 15$

2. Subtract 9 from both sides: $x + 9 - 9 = 15 - 9$, which simplifies to $x = 6$

The goal is to solve the equation $4 = 3y$ to find the value of $y$. To do this, we can follow these steps:

• Step 1: Divide both sides of the equation by 3 to isolate $y$.
• Step 2: Simplify the result to solve for $y$.

Now, let's work through the solution:

Step 1: We start with the equation:

$4 = 3y$

To solve for $y$, divide both sides by 3:

$y = \frac{4}{3}$

Step 2: Simplify the fraction:

$y = \frac{4}{3} = 1 \frac{1}{3}$

Therefore, the solution to the equation is $y = 1 \frac{1}{3}$.

This corresponds to choice $y = 1\frac{1}{3}$ in the provided multiple-choice answers.

To find the value of $a$, we must solve the given linear equation:

$11 = a - 16$

We aim to isolate $a$ by performing operations that maintain the balance of the equation. Currently, $a$ is being decreased by 16. To reverse this, we need to add 16 to both sides.

Step-by-step:

• Start with the given equation: $11 = a - 16$.
• Add 16 to both sides to start isolating $a$:

$11 + 16 = a - 16 + 16$

• This simplifies to:

$27 = a$

Thus, the value of $a$ is 27.

Therefore, the solution to the equation $11 = a - 16$ is $a = 27$.