Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+14}& = &12 \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14} & = &12\color{blue}{-14} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{-3}& = &-4 \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3} & = &-4\color{blue}{+3} \\\Leftrightarrow &x & = &-1\\\Leftrightarrow & \color{red}{}x & = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-7}& = &-3 \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7} & = &-3\color{blue}{+7} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-8}& = &5 \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8} & = &5\color{blue}{+8} \\\Leftrightarrow &-5x & = &13\\\Leftrightarrow & \color{red}{-5}x & = &13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-9}& = &3 \\\Leftrightarrow & 2x \color{red}{-9}\color{blue}{+9} & = &3\color{blue}{+9} \\\Leftrightarrow &2x & = &12\\\Leftrightarrow & \color{red}{2}x & = &12\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{12}{2} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+11}& = &-12 \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11} & = &-12\color{blue}{-11} \\\Leftrightarrow &8x & = &-23\\\Leftrightarrow & \color{red}{8}x & = &-23\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-23}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{8} } & & \\ & V = \left\{ \frac{-23}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+1}& = &-9 \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1} & = &-9\color{blue}{-1} \\\Leftrightarrow &2x & = &-10\\\Leftrightarrow & \color{red}{2}x & = &-10\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-10}{2} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+11}& = &10 \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11} & = &10\color{blue}{-11} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+8}& = &-12 \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8} & = &-12\color{blue}{-8} \\\Leftrightarrow &5x & = &-20\\\Leftrightarrow & \color{red}{5}x & = &-20\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-20}{5} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-13}& = &8 \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13} & = &8\color{blue}{+13} \\\Leftrightarrow &-12x & = &21\\\Leftrightarrow & \color{red}{-12}x & = &21\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{21}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-11}& = &12 \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11} & = &12\color{blue}{+11} \\\Leftrightarrow &-x & = &23\\\Leftrightarrow & \color{red}{-}x & = &23\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{23}{-1} \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+8}& = &-9 \\\Leftrightarrow & -9x \color{red}{+8}\color{blue}{-8} & = &-9\color{blue}{-8} \\\Leftrightarrow &-9x & = &-17\\\Leftrightarrow & \color{red}{-9}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-17}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{17}{9} } & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)