Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+3}& = &-4 \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3} & = &-4\color{blue}{-3} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+12}& = &4 \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12} & = &4\color{blue}{-12} \\\Leftrightarrow &-13x & = &-8\\\Leftrightarrow & \color{red}{-13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+2}& = &-14 \\\Leftrightarrow & -5x \color{red}{+2}\color{blue}{-2} & = &-14\color{blue}{-2} \\\Leftrightarrow &-5x & = &-16\\\Leftrightarrow & \color{red}{-5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+4}& = &5 \\\Leftrightarrow & 5x \color{red}{+4}\color{blue}{-4} & = &5\color{blue}{-4} \\\Leftrightarrow &5x & = &1\\\Leftrightarrow & \color{red}{5}x & = &1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+1}& = &4 \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1} & = &4\color{blue}{-1} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-10}& = &-4 \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10} & = &-4\color{blue}{+10} \\\Leftrightarrow &-15x & = &6\\\Leftrightarrow & \color{red}{-15}x & = &6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-15}& = &15 \\\Leftrightarrow & -8x \color{red}{-15}\color{blue}{+15} & = &15\color{blue}{+15} \\\Leftrightarrow &-8x & = &30\\\Leftrightarrow & \color{red}{-8}x & = &30\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{30}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{4} } & & \\ & V = \left\{ \frac{-15}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+3}& = &-1 \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3} & = &-1\color{blue}{-3} \\\Leftrightarrow &-8x & = &-4\\\Leftrightarrow & \color{red}{-8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-13}& = &4 \\\Leftrightarrow & 13x \color{red}{-13}\color{blue}{+13} & = &4\color{blue}{+13} \\\Leftrightarrow &13x & = &17\\\Leftrightarrow & \color{red}{13}x & = &17\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{17}{13} \\\Leftrightarrow & \color{green}{ x = \frac{17}{13} } & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+2}& = &14 \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2} & = &14\color{blue}{-2} \\\Leftrightarrow &5x & = &12\\\Leftrightarrow & \color{red}{5}x & = &12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-4}& = &-12 \\\Leftrightarrow & -6x \color{red}{-4}\color{blue}{+4} & = &-12\color{blue}{+4} \\\Leftrightarrow &-6x & = &-8\\\Leftrightarrow & \color{red}{-6}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-2}& = &-1 \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2} & = &-1\color{blue}{+2} \\\Leftrightarrow &-14x & = &1\\\Leftrightarrow & \color{red}{-14}x & = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)