Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-9}& = &8 \\\Leftrightarrow & -15x \color{red}{-9}\color{blue}{+9} & = &8\color{blue}{+9} \\\Leftrightarrow &-15x & = &17\\\Leftrightarrow & \color{red}{-15}x & = &17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{15} } & & \\ & V = \left\{ \frac{-17}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+10}& = &-7 \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10} & = &-7\color{blue}{-10} \\\Leftrightarrow &-11x & = &-17\\\Leftrightarrow & \color{red}{-11}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-9}& = &-8 \\\Leftrightarrow & 5x \color{red}{-9}\color{blue}{+9} & = &-8\color{blue}{+9} \\\Leftrightarrow &5x & = &1\\\Leftrightarrow & \color{red}{5}x & = &1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+11}& = &8 \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11} & = &8\color{blue}{-11} \\\Leftrightarrow &5x & = &-3\\\Leftrightarrow & \color{red}{5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{+12}& = &6 \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12} & = &6\color{blue}{-12} \\\Leftrightarrow &2x & = &-6\\\Leftrightarrow & \color{red}{2}x & = &-6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-6}{2} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+10}& = &14 \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10} & = &14\color{blue}{-10} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-2}& = &-3 \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2} & = &-3\color{blue}{+2} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-4}& = &14 \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4} & = &14\color{blue}{+4} \\\Leftrightarrow &4x & = &18\\\Leftrightarrow & \color{red}{4}x & = &18\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{18}{4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+13}& = &10 \\\Leftrightarrow & 12x \color{red}{+13}\color{blue}{-13} & = &10\color{blue}{-13} \\\Leftrightarrow &12x & = &-3\\\Leftrightarrow & \color{red}{12}x & = &-3\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-3}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+7}& = &-8 \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7} & = &-8\color{blue}{-7} \\\Leftrightarrow &-4x & = &-15\\\Leftrightarrow & \color{red}{-4}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-15}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{15}{4} } & & \\ & V = \left\{ \frac{15}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-8}& = &12 \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8} & = &12\color{blue}{+8} \\\Leftrightarrow &-15x & = &20\\\Leftrightarrow & \color{red}{-15}x & = &20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-8}& = &-12 \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8} & = &-12\color{blue}{+8} \\\Leftrightarrow &5x & = &-4\\\Leftrightarrow & \color{red}{5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)