Solving Equations Using All Methods - Examples, Exercises and Solutions

We use the formula:

$a\cdot x=b$

$x=\frac{b}{a}$

Note that the coefficient of X is 3.

Therefore, we will divide both sides by 3:

$\frac{3x}{3}=\frac{18}{3}$

Then divide accordingly:

$x=6$

To solve the equation $x + 7 = 14$, we aim to find the value of $x$ by isolating it on one side.

• Step 1: Identify the current equation: $x + 7 = 14$.
• Step 2: To isolate $x$, perform the inverse operation. Subtract 7 from both sides to maintain equality.
• Step 3: Simplify both sides: $x + 7 - 7 = 14 - 7$.
• Step 4: This simplifies to $x = 7$.

Therefore, we have found that the solution to the equation $x + 7 = 14$ is $x = 7$, which matches the given answer choice 2.

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 $x = 6$

To solve for $x$, start by isolating $x$ on one side of the equation:
Subtract 7 from both sides:
$x + 7 - 7 = 12 - 7$ simplifies to
$x = 5$.

To solve for $x$, start by isolating $x$ on one side of the equation:
Subtract 8 from both sides:
$x + 8 - 8 = 10 - 8$ simplifies to
$x = 2$.

To solve for $x$, start by isolating $x$ on one side of the equation:
Subtract 3 from both sides:
$x + 3 - 3 = 7 - 3$ simplifies to
$x = 4$.

To solve the equation $x - 5 = -10$, we need to isolate $x$.

Step 1: Add 5 to both sides of the equation to cancel out the -5 on the left side.
$x - 5 + 5 = -10 + 5$
Step 2: Simplify both sides.
$x = -5$
Thus, the solution is $x = -5$.

To solve the equation $x + 9 = 3$, we need to isolate $x$.

Step 1: Subtract 9 from both sides of the equation to cancel out the +9 on the left side.
$x + 9 - 9 = 3 - 9$
Step 2: Simplify both sides.
$x = -6$
Thus, the solution is $x = -6$.

To solve the equation $x - 7 = 14$, we need to isolate $x$.

Step 1: Add 7 to both sides of the equation to cancel out the -7 on the left side.
$x - 7 + 7 = 14 + 7$
Step 2: Simplify both sides.
$x = 21$
Thus, the solution is $x = 21$.

To solve for $y$, we need to isolate it on one side of the equation. Starting with:

$y-4=9$

Add $4$ to both sides to get:

$y-4+4=9+4$

This simplifies to:

$y=13$

Therefore, the solution is $y = 13$.

To solve for $a$, we need to isolate it on one side of the equation. Starting with:

$a-5=10$

Add $5$ to both sides to get:

$a-5+5=10+5$

This simplifies to:

$a=15$

Therefore, the solution is$a = 15$.

To solve for $b$, we need to isolate it on one side of the equation. Starting with:

$b+6=14$

Subtract$6$ from both sides to get:

$b+6-6=14-6$

This simplifies to:

$b=8$

Therefore, the solution is $b = 8$.

To solve for $x$, we need to isolate it on one side of the equation. Starting with:

$x+7=12$

Subtract$7$ from both sides to get:

$x+7-7=12-7$

This simplifies to:

$x=5$

Therefore, the solution is $x = 5$.

To solve for $z$, we need to isolate it on one side of the equation. Starting with:

$z+2=8$

Subtract $2$ from both sides to get:

$z+2-2=8-2$

This simplifies to:

$z=6$

Therefore, the solution is $z = 6$.

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.