Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+8}& = &8 \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8} & = &8\color{blue}{-8} \\\Leftrightarrow &-10x & = &0\\\Leftrightarrow & \color{red}{-10}x & = &0\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{0}{-10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+15}& = &6 \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15} & = &6\color{blue}{-15} \\\Leftrightarrow &-5x & = &-9\\\Leftrightarrow & \color{red}{-5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+9}& = &11 \\\Leftrightarrow & -3x \color{red}{+9}\color{blue}{-9} & = &11\color{blue}{-9} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+7}& = &3 \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7} & = &3\color{blue}{-7} \\\Leftrightarrow &10x & = &-4\\\Leftrightarrow & \color{red}{10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+14}& = &-3 \\\Leftrightarrow & 5x \color{red}{+14}\color{blue}{-14} & = &-3\color{blue}{-14} \\\Leftrightarrow &5x & = &-17\\\Leftrightarrow & \color{red}{5}x & = &-17\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-17}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{5} } & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+12}& = &13 \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12} & = &13\color{blue}{-12} \\\Leftrightarrow &8x & = &1\\\Leftrightarrow & \color{red}{8}x & = &1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-12}& = &11 \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12} & = &11\color{blue}{+12} \\\Leftrightarrow &11x & = &23\\\Leftrightarrow & \color{red}{11}x & = &23\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{23}{11} \\\Leftrightarrow & \color{green}{ x = \frac{23}{11} } & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-14}& = &1 \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14} & = &1\color{blue}{+14} \\\Leftrightarrow &-2x & = &15\\\Leftrightarrow & \color{red}{-2}x & = &15\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{15}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{2} } & & \\ & V = \left\{ \frac{-15}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+4}& = &-11 \\\Leftrightarrow & x \color{red}{+4}\color{blue}{-4} & = &-11\color{blue}{-4} \\\Leftrightarrow &x & = &-15\\\Leftrightarrow & \color{red}{}x & = &-15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -15 \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-7}& = &-1 \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7} & = &-1\color{blue}{+7} \\\Leftrightarrow &-6x & = &6\\\Leftrightarrow & \color{red}{-6}x & = &6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{6}{-6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+6}& = &13 \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6} & = &13\color{blue}{-6} \\\Leftrightarrow &13x & = &7\\\Leftrightarrow & \color{red}{13}x & = &7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-1}& = &3 \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1} & = &3\color{blue}{+1} \\\Leftrightarrow &-14x & = &4\\\Leftrightarrow & \color{red}{-14}x & = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)