Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+12}& = &14 \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12} & = &14\color{blue}{-12} \\\Leftrightarrow &-8x & = &2\\\Leftrightarrow & \color{red}{-8}x & = &2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+2}& = &-11 \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2} & = &-11\color{blue}{-2} \\\Leftrightarrow &-15x & = &-13\\\Leftrightarrow & \color{red}{-15}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{13}{15} } & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-14}& = &13 \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14} & = &13\color{blue}{+14} \\\Leftrightarrow &-7x & = &27\\\Leftrightarrow & \color{red}{-7}x & = &27\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{27}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{7} } & & \\ & V = \left\{ \frac{-27}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-7}& = &-1 \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7} & = &-1\color{blue}{+7} \\\Leftrightarrow &7x & = &6\\\Leftrightarrow & \color{red}{7}x & = &6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-8}& = &-4 \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8} & = &-4\color{blue}{+8} \\\Leftrightarrow &10x & = &4\\\Leftrightarrow & \color{red}{10}x & = &4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+2}& = &15 \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2} & = &15\color{blue}{-2} \\\Leftrightarrow &-9x & = &13\\\Leftrightarrow & \color{red}{-9}x & = &13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-6}& = &9 \\\Leftrightarrow & 11x \color{red}{-6}\color{blue}{+6} & = &9\color{blue}{+6} \\\Leftrightarrow &11x & = &15\\\Leftrightarrow & \color{red}{11}x & = &15\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{15}{11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+9}& = &-13 \\\Leftrightarrow & 5x \color{red}{+9}\color{blue}{-9} & = &-13\color{blue}{-9} \\\Leftrightarrow &5x & = &-22\\\Leftrightarrow & \color{red}{5}x & = &-22\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-22}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{5} } & & \\ & V = \left\{ \frac{-22}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-15}& = &3 \\\Leftrightarrow & -8x \color{red}{-15}\color{blue}{+15} & = &3\color{blue}{+15} \\\Leftrightarrow &-8x & = &18\\\Leftrightarrow & \color{red}{-8}x & = &18\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{18}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-2}& = &-14 \\\Leftrightarrow & 12x \color{red}{-2}\color{blue}{+2} & = &-14\color{blue}{+2} \\\Leftrightarrow &12x & = &-12\\\Leftrightarrow & \color{red}{12}x & = &-12\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-12}{12} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+6}& = &12 \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6} & = &12\color{blue}{-6} \\\Leftrightarrow &-2x & = &6\\\Leftrightarrow & \color{red}{-2}x & = &6\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{6}{-2} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+14}& = &-6 \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14} & = &-6\color{blue}{-14} \\\Leftrightarrow &-13x & = &-20\\\Leftrightarrow & \color{red}{-13}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)