Question1. Solve each of the following equations for all value(s) of $x$ . (a) $(x-2)(x+5)=0$ (b) $(7 x-1)(2 x+5)=0$ (c) $(3 x-1)(3 x+1)=0$

Studdy Solution

STEP 1

What is this asking? We need to find the values of $x$ that make each of these equations true. Watch out! Remember that if several things multiplied together equal zero, at least one of them must be zero!

STEP 2

1. Solve equation (a)
2. Solve equation (b)
3. Solve equation (c)

STEP 3

We're given the equation $(x-2)(x+5)=0$ .
Since the product equals zero, either the first part or the second part (or both!) must be zero.
This gives us two possibilities to explore!

STEP 4

First possibility: $x-2=0$ .
To isolate $x$ , we can add $2$ to both sides of the equation: $x - 2 + 2 = 0 + 2$ , which simplifies to $x=2$ .

STEP 5

Second possibility: $x+5=0$ .
To isolate $x$ , we subtract $5$ from both sides: $x + 5 - 5 = 0 - 5$ , which simplifies to $x=-5$ .

STEP 6

So, the solutions for equation (a) are $x=\mathbf{2}$ and $x=\mathbf{-5}$ !

STEP 7

We have $(7x-1)(2x+5)=0$ .
Again, either $7x-1=0$ or $2x+5=0$ (or both!).

STEP 8

First possibility: $7x-1=0$ . Add $1$ to both sides: $7x - 1 + 1 = 0 + 1$ , so $7x=1$ .
Now, divide both sides by $7$ : $7x \cdot \frac{1}{7} = 1 \cdot \frac{1}{7}$ , which means $x=\mathbf{\frac{1}{7}}$ .

STEP 9

Second possibility: $2x+5=0$ . Subtract $5$ from both sides: $2x + 5 - 5 = 0 - 5$ , so $2x=-5$ . Divide both sides by $2$ : $2x \cdot \frac{1}{2} = -5 \cdot \frac{1}{2}$ , giving us $x=\mathbf{-\frac{5}{2}}$ .

STEP 10

Therefore, the solutions for equation (b) are $x=\mathbf{\frac{1}{7}}$ and $x=\mathbf{-\frac{5}{2}}$ !

STEP 11

We're looking at $(3x-1)(3x+1)=0$ .
So, either $3x-1=0$ or $3x+1=0$ (or both!).

STEP 12

First possibility: $3x-1=0$ . Add $1$ to both sides: $3x - 1 + 1 = 0 + 1$ , so $3x=1$ . Divide both sides by $3$ : $3x \cdot \frac{1}{3} = 1 \cdot \frac{1}{3}$ , which means $x=\mathbf{\frac{1}{3}}$ .

STEP 13

Second possibility: $3x+1=0$ . Subtract $1$ from both sides: $3x + 1 - 1 = 0 - 1$ , so $3x=-1$ . Divide both sides by $3$ : $3x \cdot \frac{1}{3} = -1 \cdot \frac{1}{3}$ , giving us $x=\mathbf{-\frac{1}{3}}$ .

STEP 14

The solutions for equation (c) are $x=\mathbf{\frac{1}{3}}$ and $x=\mathbf{-\frac{1}{3}}$ !

STEP 15

The solutions are: (a) $x=2$ and $x=-5$ (b) $x=\frac{1}{7}$ and $x=-\frac{5}{2}$ (c) $x=\frac{1}{3}$ and $x=-\frac{1}{3}$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms