Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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