Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

1. \(-7x+7=14\)
2. \(-5x-3=3\)
3. \(5x-11=9\)
4. \(10x-9=15\)
5. \(-8x-7=13\)
6. \(8x+6=11\)
7. \(5x-2=7\)
8. \(11x+8=-14\)
9. \(-10x+8=2\)
10. \(2x-5=-7\)
11. \(-15x+3=9\)
12. \(13x+8=-14\)

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+7}& = &14 \\\Leftrightarrow & -7x \color{red}{+7}\color{blue}{-7} & = &14\color{blue}{-7} \\\Leftrightarrow &-7x & = &7\\\Leftrightarrow & \color{red}{-7}x & = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{-3}& = &3 \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3} & = &3\color{blue}{+3} \\\Leftrightarrow &-5x & = &6\\\Leftrightarrow & \color{red}{-5}x & = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-11}& = &9 \\\Leftrightarrow & 5x \color{red}{-11}\color{blue}{+11} & = &9\color{blue}{+11} \\\Leftrightarrow &5x & = &20\\\Leftrightarrow & \color{red}{5}x & = &20\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{20}{5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-9}& = &15 \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9} & = &15\color{blue}{+9} \\\Leftrightarrow &10x & = &24\\\Leftrightarrow & \color{red}{10}x & = &24\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{24}{10} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-7}& = &13 \\\Leftrightarrow & -8x \color{red}{-7}\color{blue}{+7} & = &13\color{blue}{+7} \\\Leftrightarrow &-8x & = &20\\\Leftrightarrow & \color{red}{-8}x & = &20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+6}& = &11 \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6} & = &11\color{blue}{-6} \\\Leftrightarrow &8x & = &5\\\Leftrightarrow & \color{red}{8}x & = &5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-2}& = &7 \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2} & = &7\color{blue}{+2} \\\Leftrightarrow &5x & = &9\\\Leftrightarrow & \color{red}{5}x & = &9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{+8}& = &-14 \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8} & = &-14\color{blue}{-8} \\\Leftrightarrow &11x & = &-22\\\Leftrightarrow & \color{red}{11}x & = &-22\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-22}{11} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+8}& = &2 \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8} & = &2\color{blue}{-8} \\\Leftrightarrow &-10x & = &-6\\\Leftrightarrow & \color{red}{-10}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-5}& = &-7 \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5} & = &-7\color{blue}{+5} \\\Leftrightarrow &2x & = &-2\\\Leftrightarrow & \color{red}{2}x & = &-2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-2}{2} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+3}& = &9 \\\Leftrightarrow & -15x \color{red}{+3}\color{blue}{-3} & = &9\color{blue}{-3} \\\Leftrightarrow &-15x & = &6\\\Leftrightarrow & \color{red}{-15}x & = &6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+8}& = &-14 \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8} & = &-14\color{blue}{-8} \\\Leftrightarrow &13x & = &-22\\\Leftrightarrow & \color{red}{13}x & = &-22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{13} } & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)