Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-6}& = &-14 \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6} & = &-14\color{blue}{+6} \\\Leftrightarrow &8x & = &-8\\\Leftrightarrow & \color{red}{8}x & = &-8\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-8}{8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+8}& = &-15 \\\Leftrightarrow & -5x \color{red}{+8}\color{blue}{-8} & = &-15\color{blue}{-8} \\\Leftrightarrow &-5x & = &-23\\\Leftrightarrow & \color{red}{-5}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-23}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{23}{5} } & & \\ & V = \left\{ \frac{23}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+2}& = &7 \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2} & = &7\color{blue}{-2} \\\Leftrightarrow &9x & = &5\\\Leftrightarrow & \color{red}{9}x & = &5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-14}& = &13 \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14} & = &13\color{blue}{+14} \\\Leftrightarrow &-9x & = &27\\\Leftrightarrow & \color{red}{-9}x & = &27\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{27}{-9} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{+14}& = &-5 \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14} & = &-5\color{blue}{-14} \\\Leftrightarrow &-10x & = &-19\\\Leftrightarrow & \color{red}{-10}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-19}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{19}{10} } & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-11}& = &-13 \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11} & = &-13\color{blue}{+11} \\\Leftrightarrow &-2x & = &-2\\\Leftrightarrow & \color{red}{-2}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-2}{-2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-8}& = &5 \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8} & = &5\color{blue}{+8} \\\Leftrightarrow &9x & = &13\\\Leftrightarrow & \color{red}{9}x & = &13\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{13}{9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+11}& = &-10 \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11} & = &-10\color{blue}{-11} \\\Leftrightarrow &8x & = &-21\\\Leftrightarrow & \color{red}{8}x & = &-21\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-21}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{8} } & & \\ & V = \left\{ \frac{-21}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+4}& = &-15 \\\Leftrightarrow & 4x \color{red}{+4}\color{blue}{-4} & = &-15\color{blue}{-4} \\\Leftrightarrow &4x & = &-19\\\Leftrightarrow & \color{red}{4}x & = &-19\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-19}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{4} } & & \\ & V = \left\{ \frac{-19}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+8}& = &-14 \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8} & = &-14\color{blue}{-8} \\\Leftrightarrow &-4x & = &-22\\\Leftrightarrow & \color{red}{-4}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-22}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-2}& = &-6 \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2} & = &-6\color{blue}{+2} \\\Leftrightarrow &3x & = &-4\\\Leftrightarrow & \color{red}{3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-4}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-13}& = &-14 \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13} & = &-14\color{blue}{+13} \\\Leftrightarrow &12x & = &-1\\\Leftrightarrow & \color{red}{12}x & = &-1\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-1}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)