Question

4x-8≤12

Answer 1

solve the equation and write the answer using set notation
14/x-2 = 7 and x ≠ 2

Answer 2

rearrange to highlight h
A=b*h

Answer 3

To solve the inequality \( 4x - 8 \leq 12 \), follow these steps:

1. **Add 8 to both sides**:
\[
4x - 8 + 8 \leq 12 + 8
\]
This simplifies to:
\[
4x \leq 20
\]

2. **Divide both sides by 4**:
\[
\frac{4x}{4} \leq \frac{20}{4}
\]
This simplifies to:
\[
x \leq 5
\]

So, the solution to the inequality is:
\[
x \leq 5
\]

In interval notation, this can be expressed as:
\[
(-\infty, 5]
\]

Answer 4

To solve the equation

\[
\frac{14}{x} - 2 = 7,
\]

follow these steps:

1. **Isolate the term with \(x\)**:
Add 2 to both sides of the equation:
\[
\frac{14}{x} = 7 + 2
\]
This simplifies to:
\[
\frac{14}{x} = 9.
\]

2. **Multiply both sides by \(x\)** (note that \(x \neq 0\) to avoid division by zero):
\[
14 = 9x.
\]

3. **Solve for \(x\)**:
Divide both sides by 9:
\[
x = \frac{14}{9}.
\]

Since the problem states that \(x \neq 2\), we check if our solution \(\frac{14}{9}\) is equal to 2. Since \(\frac{14}{9} \approx 1.56\), which is not equal to 2, it satisfies the \(x \neq 2\) condition.

Thus, the solution to the equation is

\[
\left\{ \frac{14}{9} \right\}.
\]

Using set notation, the final answer is:
\[
\{ \frac{14}{9} \}.
\]

Answer 5

To rearrange the equation \( A = b \cdot h \) to highlight \( h \), follow these steps:

1. **Isolate \( h \)**: Divide both sides of the equation by \( b \) (assuming \( b \neq 0 \)):
\[
h = \frac{A}{b}.
\]

Now, the equation is rearranged to highlight \( h \):
\[
h = \frac{A}{b}.
\]