1.
a)
[tex]5x + 6 = 8 \\ 5x = 8 - 6 | \div 5 \\ x = \frac{8 - 6}{5} [/tex]
[tex]ax + b = c \\ ax = c - b | \div a \\ x = \frac{c - b}{a} [/tex]
b)
[tex] \frac{x - 1}{3} = 4 | \times 3 \\ x - 1 = 4 \times 3 \\ x = 4 \times 3 + 1[/tex]
[tex] \frac{x - a}{b} = c | \times b \\ x - a = c \times b \\ x = c \times b + a[/tex]
c)
[tex] \frac{5 + x}{2} = 3 | \times 2 \\5 + x = 3 \times 2 \\ x = 3 \times 2 - 5[/tex]
[tex] \frac{a + x}{b} = c | \times b \\ a + x = c \times b \\ x = c \times b - a[/tex]
d)
[tex]5 = \frac{2}{x} | \times x \\ 5 \times x = 2 | \div 5 \\ x = \frac{2}{5} [/tex]
[tex]a = \frac{ b }{x} | \times x \\ a \times x = b \\ x = \frac{b}{a} [/tex]
2.
a)
[tex]v = \frac{s}{t} | \times t \\ s = v \times t[/tex]
b)
[tex]v = \frac{s}{t} | \times t \\ s = v \times t | \div v \\ t = \frac{s}{v} [/tex]
3.
a)
[tex]E = \frac{1}{2} {mv}^{2} | \times 2 \\ 2E = {mv}^{2} | \div {v}^{2} \\ m = \frac{2E}{ {v}^{2} } [/tex]
b)
[tex]E = \frac{1}{2} {mv}^{2} | \times 2 \\ 2E = {mv}^{2} | \div m \\ {v}^{2} = \frac{2E}{m} \\ v = \sqrt{ \frac{2E}{m} } [/tex]
