Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

1. \(13x-4=5\)
2. \(9x+5=5\)
3. \(-8x+8=6\)
4. \(-10x-8=13\)
5. \(-2x+13=5\)
6. \(8x+8=13\)
7. \(6x+10=3\)
8. \(-11x-5=7\)
9. \(-10x-9=-1\)
10. \(10x+15=-2\)
11. \(-6x+1=13\)
12. \(-3x+3=-7\)

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-4}& = &5 \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4} & = &5\color{blue}{+4} \\\Leftrightarrow &13x & = &9\\\Leftrightarrow & \color{red}{13}x & = &9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+5}& = &5 \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5} & = &5\color{blue}{-5} \\\Leftrightarrow &9x & = &0\\\Leftrightarrow & \color{red}{9}x & = &0\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{0}{9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+8}& = &6 \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8} & = &6\color{blue}{-8} \\\Leftrightarrow &-8x & = &-2\\\Leftrightarrow & \color{red}{-8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-8}& = &13 \\\Leftrightarrow & -10x \color{red}{-8}\color{blue}{+8} & = &13\color{blue}{+8} \\\Leftrightarrow &-10x & = &21\\\Leftrightarrow & \color{red}{-10}x & = &21\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{21}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{10} } & & \\ & V = \left\{ \frac{-21}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+13}& = &5 \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13} & = &5\color{blue}{-13} \\\Leftrightarrow &-2x & = &-8\\\Leftrightarrow & \color{red}{-2}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-8}{-2} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+8}& = &13 \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8} & = &13\color{blue}{-8} \\\Leftrightarrow &8x & = &5\\\Leftrightarrow & \color{red}{8}x & = &5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+10}& = &3 \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10} & = &3\color{blue}{-10} \\\Leftrightarrow &6x & = &-7\\\Leftrightarrow & \color{red}{6}x & = &-7\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-7}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-5}& = &7 \\\Leftrightarrow & -11x \color{red}{-5}\color{blue}{+5} & = &7\color{blue}{+5} \\\Leftrightarrow &-11x & = &12\\\Leftrightarrow & \color{red}{-11}x & = &12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{11} } & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-9}& = &-1 \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9} & = &-1\color{blue}{+9} \\\Leftrightarrow &-10x & = &8\\\Leftrightarrow & \color{red}{-10}x & = &8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+15}& = &-2 \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15} & = &-2\color{blue}{-15} \\\Leftrightarrow &10x & = &-17\\\Leftrightarrow & \color{red}{10}x & = &-17\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-17}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{10} } & & \\ & V = \left\{ \frac{-17}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+1}& = &13 \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1} & = &13\color{blue}{-1} \\\Leftrightarrow &-6x & = &12\\\Leftrightarrow & \color{red}{-6}x & = &12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{12}{-6} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{+3}& = &-7 \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3} & = &-7\color{blue}{-3} \\\Leftrightarrow &-3x & = &-10\\\Leftrightarrow & \color{red}{-3}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)