Question

3(x+2)-x=10 4x+3(x-7)=58=3(x-4)-x3x(x-1)+x=2x1/8-1/64 x=0-1/4x-1/2=0t×4/31=28/31​

Answer 1

1) x = 2

$3(x + 2) - x = 10 \\ 3x + 6 - x = 10 \\ 3x - x = 10 - 6 \\ 2x = 4 \\ x = 4 \div 2 = 2$

2) x = 26/7 = 3 5/7

$4x + 3(x - 7) = 5 \\ 4x + 3x - 21 = 5 \\ 7x = 5 + 21 = 26 \\ x = \frac{26}{7}$

3) x = 10

$8 = 3(x - 4) - x \\ 8 = 3x - 12 - x \\ 8 = 2x - 12 \\ 2x = 8 + 12 = 20 \\ x = 20 \div 2 = 10$

4) x = 3/2

$3(x - 1) + x = 2x \\ 3x - 3 + x = 2x \\ 2x = 3 \\ x = \frac{3}{2}$

5) x = 8

$\frac{1}{8} - \frac{1}{64} x = 0 \\ \frac{1}{8} = \frac{1}{64} x \\ x = \frac{1}{8} \div \frac{1}{64} = \frac{1}{8} \times \frac{64}{1} \\ x = 8$

6) x = -2

$- \frac{1}{4} x - \frac{1}{2} = 0 \\ - \frac{1}{4} x = \frac{1}{2} \\ x = \frac{1}{2} \div ( - \frac{1}{4} ) = \frac{1}{2} \times ( - \frac{4}{1} ) \\ x = - 2$

7) t = 7

$t \times \frac{4}{31} = \frac{28}{31} \\ t = \frac{28}{31} \div \frac{4}{31} = \frac{28}{31} \times \frac{31}{4} \\ t = 7$

Answer 2

Let's solve each equation step by step:

1. Equation 1: 3(x + 2) - x = 10

Expanding the brackets:

3x + 6 - x = 10

Combining like terms:

2x + 6 = 10

Subtracting 6 from both sides:

2x = 4

Dividing both sides by 2:

x = 2

So, the solution for Equation 1 is x = 2.

2. Equation 2: 4x + 3(x - 7) = 58

Expanding the brackets:

4x + 3x - 21 = 58

Combining like terms:

7x - 21 = 58

Adding 21 to both sides:

7x = 79

Dividing both sides by 7:

x = 79/7

Simplifying:

x = 11.2857 (rounded to four decimal places)

So, the solution for Equation 2 is x = 11.2857.

3. Equation 3: 3x(x - 1) + x = 2x

Expanding the brackets:

3x^2 - 3x + x = 2x

Combining like terms:

3x^2 - 2x = 2x

Subtracting 2x from both sides:

3x^2 - 4x = 0

Factoring out an x:

x(3x - 4) = 0

Using the zero-product property, we have two possibilities:

x = 0 or 3x - 4 = 0

For the second equation, adding 4 to both sides:

3x = 4

Dividing both sides by 3:

x = 4/3

So, the solutions for Equation 3 are x = 0 and x = 4/3.

4. Equation 4: 1/8 - 1/64x - 1/2 = 0

Combining like terms, we get:

1/8 - 1/64x = 1/2

Multiplying both sides by 64x to eliminate the denominator:

8x - 1 = 32x

Subtracting 8x from both sides:

-1 = 24x

Dividing both sides by 24:

x = -1/24

So, the solution for Equation 4 is x = -1/24.

5. Equation 5: t * 4/31 = 28/31

To isolate t, we need to divide both sides by 4/31:

t = (28/31) / (4/31)

Simplifying:

t = (28/31) * (31/4)

Canceling out the common factors:

t = 7

So, the solution for Equation 5 is t = 7.