Evaluate 1001(two) - 110(two)

1.

$10(x + 3) = 11(x + 1)$

Step 1: Expand both sides.
$10x + 30 = 11x + 11$

Step 2: Subtract $10x$ from both sides.
$30 = x + 11$

Step 3: Subtract $11$ from both sides.
$30 - 11 = x$
$19 = x$

x = 19
19

2.

$11101101_2$

Step 1: Write powers of 2 from right to left.
$2^7 \quad 2^6 \quad 2^5 \quad 2^4 \quad 2^3 \quad 2^2 \quad 2^1 \quad 2^0$
$128 \quad 64 \quad 32 \quad 16 \quad 8 \quad 4 \quad 2 \quad 1$
$1 \quad\quad 1 \quad\quad 1 \quad\quad 0 \quad\quad 1 \quad\quad 1 \quad\quad 0 \quad\quad 1$

Step 2: Multiply and sum.
$128 \times 1 + 64 \times 1 + 32 \times 1 + 16 \times 0 + 8 \times 1 + 4 \times 1 + 2 \times 0 + 1 \times 1$
$128 + 64 + 32 + 0 + 8 + 4 + 0 + 1$

Step 3: Add step-by-step.
$128 + 64 = 192$
$192 + 32 = 224$
$224 + 8 = 232$
$232 + 4 = 236$
$236 + 1 = 237$

237 (denary)
237

3.

247 (denary)

Step 1: Divide by 2 and record remainders.
$247 \div 2 = 123,\ remainder\ 1$
$123 \div 2 = 61,\ remainder\ 1$
$61 \div 2 = 30,\ remainder\ 1$
$30 \div 2 = 15,\ remainder\ 0$
$15 \div 2 = 7,\ remainder\ 1$
$7 \div 2 = 3,\ remainder\ 1$
$3 \div 2 = 1,\ remainder\ 1$
$1 \div 2 = 0,\ remainder\ 1$

Step 2: Read remainders from bottom to top.
$11110111_2$

11110111₂
11110111_2

4.

$3x^2 - 5x - 2 = 0$

Step 1: Factorise.
$(3x + 1)(x - 2) = 0$

Step 2: Set each factor to zero.
$3x + 1 = 0$ or $x - 2 = 0$

Step 3: Solve each equation.
$3x = -1$
$x = -\frac{1}{3}$
and
$x = 2$

x = 2 or x = -\frac{1}{3}
x=2\or\x=-\dfrac{1{3}}