Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-10}& = &-8 \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10} & = &-8\color{blue}{+10} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+2}& = &7 \\\Leftrightarrow & 8x \color{red}{+2}\color{blue}{-2} & = &7\color{blue}{-2} \\\Leftrightarrow &8x & = &5\\\Leftrightarrow & \color{red}{8}x & = &5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-13}& = &11 \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13} & = &11\color{blue}{+13} \\\Leftrightarrow &-4x & = &24\\\Leftrightarrow & \color{red}{-4}x & = &24\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{24}{-4} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+11}& = &-4 \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11} & = &-4\color{blue}{-11} \\\Leftrightarrow &-6x & = &-15\\\Leftrightarrow & \color{red}{-6}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-3}& = &-15 \\\Leftrightarrow & -8x \color{red}{-3}\color{blue}{+3} & = &-15\color{blue}{+3} \\\Leftrightarrow &-8x & = &-12\\\Leftrightarrow & \color{red}{-8}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+15}& = &-9 \\\Leftrightarrow & -14x \color{red}{+15}\color{blue}{-15} & = &-9\color{blue}{-15} \\\Leftrightarrow &-14x & = &-24\\\Leftrightarrow & \color{red}{-14}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-24}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+7}& = &-10 \\\Leftrightarrow & 11x \color{red}{+7}\color{blue}{-7} & = &-10\color{blue}{-7} \\\Leftrightarrow &11x & = &-17\\\Leftrightarrow & \color{red}{11}x & = &-17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+12}& = &-3 \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12} & = &-3\color{blue}{-12} \\\Leftrightarrow &3x & = &-15\\\Leftrightarrow & \color{red}{3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-15}{3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-15}& = &-11 \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15} & = &-11\color{blue}{+15} \\\Leftrightarrow &10x & = &4\\\Leftrightarrow & \color{red}{10}x & = &4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-13}& = &7 \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13} & = &7\color{blue}{+13} \\\Leftrightarrow &-3x & = &20\\\Leftrightarrow & \color{red}{-3}x & = &20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-2}& = &3 \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2} & = &3\color{blue}{+2} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+7}& = &-5 \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7} & = &-5\color{blue}{-7} \\\Leftrightarrow &5x & = &-12\\\Leftrightarrow & \color{red}{5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)