Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+8}& = &2 \\\Leftrightarrow & -15x \color{red}{+8}\color{blue}{-8} & = &2\color{blue}{-8} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+10}& = &-8 \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10} & = &-8\color{blue}{-10} \\\Leftrightarrow &9x & = &-18\\\Leftrightarrow & \color{red}{9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-18}{9} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+8}& = &13 \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8} & = &13\color{blue}{-8} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-13}& = &12 \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13} & = &12\color{blue}{+13} \\\Leftrightarrow &-4x & = &25\\\Leftrightarrow & \color{red}{-4}x & = &25\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{25}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{4} } & & \\ & V = \left\{ \frac{-25}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-12}& = &-4 \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12} & = &-4\color{blue}{+12} \\\Leftrightarrow &-13x & = &8\\\Leftrightarrow & \color{red}{-13}x & = &8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-10}& = &6 \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10} & = &6\color{blue}{+10} \\\Leftrightarrow &12x & = &16\\\Leftrightarrow & \color{red}{12}x & = &16\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{16}{12} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+7}& = &12 \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7} & = &12\color{blue}{-7} \\\Leftrightarrow &-10x & = &5\\\Leftrightarrow & \color{red}{-10}x & = &5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{-9}& = &-4 \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9} & = &-4\color{blue}{+9} \\\Leftrightarrow &-x & = &5\\\Leftrightarrow & \color{red}{-}x & = &5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{5}{-1} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{+8}& = &12 \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8} & = &12\color{blue}{-8} \\\Leftrightarrow &-3x & = &4\\\Leftrightarrow & \color{red}{-3}x & = &4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+15}& = &-8 \\\Leftrightarrow & x \color{red}{+15}\color{blue}{-15} & = &-8\color{blue}{-15} \\\Leftrightarrow &x & = &-23\\\Leftrightarrow & \color{red}{}x & = &-23\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -23 \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-2}& = &-2 \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2} & = &-2\color{blue}{+2} \\\Leftrightarrow &15x & = &0\\\Leftrightarrow & \color{red}{15}x & = &0\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{0}{15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-4}& = &12 \\\Leftrightarrow & -5x \color{red}{-4}\color{blue}{+4} & = &12\color{blue}{+4} \\\Leftrightarrow &-5x & = &16\\\Leftrightarrow & \color{red}{-5}x & = &16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)