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 combine all the x terms together:

$7x+4x+5x=11x+5x=16x$

The resulting equation is:

$16x=0$

Now let's divide both sides by 16:

$\frac{16x}{16}=\frac{0}{16}$

$x=\frac{0}{16}=0$

Let's first expand the parentheses using the formula:

$a(x+b)=ax+ab$

$(2\times x)+(2\times4)+8=0$

$2x+8+8=0$

Next, we will substitute in our terms accordingly:

$2x+16=0$

Then, we will move the 16 to the left-hand side, keeping the appropriate sign:

$2x=-16$

Finally, we divide both sides by 2:

$\frac{2x}{2}=-\frac{16}{2}$

$x=-8$

Let's proceed to solve the linear equation $3(a+1) - 3 = 0$:

Step 1: Distribute the 3 in the expression $3(a+1)$.

We get:
$3 \cdot a + 3 \cdot 1 - 3 = 0$

This simplifies to:
$3a + 3 - 3 = 0$

Step 2: Simplify the expression by combining like terms.

We simplify this to:
$3a + 0 = 0$ or simply $3a = 0$

Step 3: Isolate $a$ by dividing both sides by 3.

$\frac{3a}{3} = \frac{0}{3}$

Thus,
$a = 0$

Therefore, the solution to the problem is $a = 0$.

The correct choice is the option corresponding to $a = 0$.

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 $a = -1$.