Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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