Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-2}& = &9 \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2} & = &9\color{blue}{+2} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-8}& = &15 \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8} & = &15\color{blue}{+8} \\\Leftrightarrow &12x & = &23\\\Leftrightarrow & \color{red}{12}x & = &23\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{23}{12} \\\Leftrightarrow & \color{green}{ x = \frac{23}{12} } & & \\ & V = \left\{ \frac{23}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+2}& = &5 \\\Leftrightarrow & -13x \color{red}{+2}\color{blue}{-2} & = &5\color{blue}{-2} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-1}& = &-5 \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1} & = &-5\color{blue}{+1} \\\Leftrightarrow &-x & = &-4\\\Leftrightarrow & \color{red}{-}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-4}{-1} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+1}& = &3 \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1} & = &3\color{blue}{-1} \\\Leftrightarrow &-14x & = &2\\\Leftrightarrow & \color{red}{-14}x & = &2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+15}& = &3 \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15} & = &3\color{blue}{-15} \\\Leftrightarrow &-5x & = &-12\\\Leftrightarrow & \color{red}{-5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-3}& = &-10 \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3} & = &-10\color{blue}{+3} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+9}& = &7 \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9} & = &7\color{blue}{-9} \\\Leftrightarrow &7x & = &-2\\\Leftrightarrow & \color{red}{7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-7}& = &-11 \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7} & = &-11\color{blue}{+7} \\\Leftrightarrow &-6x & = &-4\\\Leftrightarrow & \color{red}{-6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-8}& = &-8 \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8} & = &-8\color{blue}{+8} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+3}& = &15 \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3} & = &15\color{blue}{-3} \\\Leftrightarrow &x & = &12\\\Leftrightarrow & \color{red}{}x & = &12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 12 \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-1}& = &-5 \\\Leftrightarrow & -4x \color{red}{-1}\color{blue}{+1} & = &-5\color{blue}{+1} \\\Leftrightarrow &-4x & = &-4\\\Leftrightarrow & \color{red}{-4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-4}{-4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)