Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+10}& = &14 \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10} & = &14\color{blue}{-10} \\\Leftrightarrow &-9x & = &4\\\Leftrightarrow & \color{red}{-9}x & = &4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+5}& = &13 \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5} & = &13\color{blue}{-5} \\\Leftrightarrow &-10x & = &8\\\Leftrightarrow & \color{red}{-10}x & = &8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-12}& = &-9 \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12} & = &-9\color{blue}{+12} \\\Leftrightarrow &9x & = &3\\\Leftrightarrow & \color{red}{9}x & = &3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-9}& = &7 \\\Leftrightarrow & 3x \color{red}{-9}\color{blue}{+9} & = &7\color{blue}{+9} \\\Leftrightarrow &3x & = &16\\\Leftrightarrow & \color{red}{3}x & = &16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-15}& = &10 \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15} & = &10\color{blue}{+15} \\\Leftrightarrow &-5x & = &25\\\Leftrightarrow & \color{red}{-5}x & = &25\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{25}{-5} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-3}& = &11 \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3} & = &11\color{blue}{+3} \\\Leftrightarrow &2x & = &14\\\Leftrightarrow & \color{red}{2}x & = &14\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{14}{2} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+7}& = &-15 \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7} & = &-15\color{blue}{-7} \\\Leftrightarrow &5x & = &-22\\\Leftrightarrow & \color{red}{5}x & = &-22\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-22}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{5} } & & \\ & V = \left\{ \frac{-22}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-5}& = &-2 \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5} & = &-2\color{blue}{+5} \\\Leftrightarrow &-12x & = &3\\\Leftrightarrow & \color{red}{-12}x & = &3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{+5}& = &13 \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5} & = &13\color{blue}{-5} \\\Leftrightarrow &-3x & = &8\\\Leftrightarrow & \color{red}{-3}x & = &8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+5}& = &14 \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5} & = &14\color{blue}{-5} \\\Leftrightarrow &3x & = &9\\\Leftrightarrow & \color{red}{3}x & = &9\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{9}{3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+4}& = &7 \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4} & = &7\color{blue}{-4} \\\Leftrightarrow &-6x & = &3\\\Leftrightarrow & \color{red}{-6}x & = &3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-11}& = &2 \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11} & = &2\color{blue}{+11} \\\Leftrightarrow &-x & = &13\\\Leftrightarrow & \color{red}{-}x & = &13\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{13}{-1} \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)