Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+8}& = &-13 \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8} & = &-13\color{blue}{-8} \\\Leftrightarrow &-11x & = &-21\\\Leftrightarrow & \color{red}{-11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+2}& = &5 \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2} & = &5\color{blue}{-2} \\\Leftrightarrow &-10x & = &3\\\Leftrightarrow & \color{red}{-10}x & = &3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-8}& = &15 \\\Leftrightarrow & -x \color{red}{-8}\color{blue}{+8} & = &15\color{blue}{+8} \\\Leftrightarrow &-x & = &23\\\Leftrightarrow & \color{red}{-}x & = &23\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{23}{-1} \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-4}& = &8 \\\Leftrightarrow & 10x \color{red}{-4}\color{blue}{+4} & = &8\color{blue}{+4} \\\Leftrightarrow &10x & = &12\\\Leftrightarrow & \color{red}{10}x & = &12\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{12}{10} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-3}& = &12 \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3} & = &12\color{blue}{+3} \\\Leftrightarrow &-12x & = &15\\\Leftrightarrow & \color{red}{-12}x & = &15\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{15}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-6}& = &11 \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6} & = &11\color{blue}{+6} \\\Leftrightarrow &14x & = &17\\\Leftrightarrow & \color{red}{14}x & = &17\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{17}{14} \\\Leftrightarrow & \color{green}{ x = \frac{17}{14} } & & \\ & V = \left\{ \frac{17}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-10}& = &3 \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10} & = &3\color{blue}{+10} \\\Leftrightarrow &-10x & = &13\\\Leftrightarrow & \color{red}{-10}x & = &13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+6}& = &15 \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6} & = &15\color{blue}{-6} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+7}& = &11 \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7} & = &11\color{blue}{-7} \\\Leftrightarrow &-5x & = &4\\\Leftrightarrow & \color{red}{-5}x & = &4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-11}& = &-5 \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11} & = &-5\color{blue}{+11} \\\Leftrightarrow &-6x & = &6\\\Leftrightarrow & \color{red}{-6}x & = &6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{6}{-6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{+4}& = &-5 \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4} & = &-5\color{blue}{-4} \\\Leftrightarrow &2x & = &-9\\\Leftrightarrow & \color{red}{2}x & = &-9\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-9}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{+11}& = &-8 \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11} & = &-8\color{blue}{-11} \\\Leftrightarrow &8x & = &-19\\\Leftrightarrow & \color{red}{8}x & = &-19\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-19}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{8} } & & \\ & V = \left\{ \frac{-19}{8} \right\} & \\\end{align}\)