Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+15}& = &9 \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15} & = &9\color{blue}{-15} \\\Leftrightarrow &8x & = &-6\\\Leftrightarrow & \color{red}{8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-6}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+14}& = &3 \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14} & = &3\color{blue}{-14} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{+15}& = &-3 \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15} & = &-3\color{blue}{-15} \\\Leftrightarrow &2x & = &-18\\\Leftrightarrow & \color{red}{2}x & = &-18\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-18}{2} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-10}& = &4 \\\Leftrightarrow & x \color{red}{-10}\color{blue}{+10} & = &4\color{blue}{+10} \\\Leftrightarrow &x & = &14\\\Leftrightarrow & \color{red}{}x & = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{-7}& = &15 \\\Leftrightarrow & 15x \color{red}{-7}\color{blue}{+7} & = &15\color{blue}{+7} \\\Leftrightarrow &15x & = &22\\\Leftrightarrow & \color{red}{15}x & = &22\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{22}{15} \\\Leftrightarrow & \color{green}{ x = \frac{22}{15} } & & \\ & V = \left\{ \frac{22}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-1}& = &14 \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1} & = &14\color{blue}{+1} \\\Leftrightarrow &-x & = &15\\\Leftrightarrow & \color{red}{-}x & = &15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{15}{-1} \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{-10}& = &-2 \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10} & = &-2\color{blue}{+10} \\\Leftrightarrow &-14x & = &8\\\Leftrightarrow & \color{red}{-14}x & = &8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-4}& = &-7 \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4} & = &-7\color{blue}{+4} \\\Leftrightarrow &14x & = &-3\\\Leftrightarrow & \color{red}{14}x & = &-3\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-3}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-9}& = &-9 \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9} & = &-9\color{blue}{+9} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-13}& = &-2 \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13} & = &-2\color{blue}{+13} \\\Leftrightarrow &5x & = &11\\\Leftrightarrow & \color{red}{5}x & = &11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{-8}& = &4 \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8} & = &4\color{blue}{+8} \\\Leftrightarrow &-8x & = &12\\\Leftrightarrow & \color{red}{-8}x & = &12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+11}& = &-13 \\\Leftrightarrow & -11x \color{red}{+11}\color{blue}{-11} & = &-13\color{blue}{-11} \\\Leftrightarrow &-11x & = &-24\\\Leftrightarrow & \color{red}{-11}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-24}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{24}{11} } & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)