Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-5}& = &15 \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5} & = &15\color{blue}{+5} \\\Leftrightarrow &8x & = &20\\\Leftrightarrow & \color{red}{8}x & = &20\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{20}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+4}& = &7 \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4} & = &7\color{blue}{-4} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+2}& = &-9 \\\Leftrightarrow & -4x \color{red}{+2}\color{blue}{-2} & = &-9\color{blue}{-2} \\\Leftrightarrow &-4x & = &-11\\\Leftrightarrow & \color{red}{-4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-1}& = &-3 \\\Leftrightarrow & 10x \color{red}{-1}\color{blue}{+1} & = &-3\color{blue}{+1} \\\Leftrightarrow &10x & = &-2\\\Leftrightarrow & \color{red}{10}x & = &-2\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-2}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-13}& = &2 \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13} & = &2\color{blue}{+13} \\\Leftrightarrow &-15x & = &15\\\Leftrightarrow & \color{red}{-15}x & = &15\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{15}{-15} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-5}& = &-1 \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5} & = &-1\color{blue}{+5} \\\Leftrightarrow &15x & = &4\\\Leftrightarrow & \color{red}{15}x & = &4\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{4}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+5}& = &4 \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5} & = &4\color{blue}{-5} \\\Leftrightarrow &3x & = &-1\\\Leftrightarrow & \color{red}{3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+8}& = &7 \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8} & = &7\color{blue}{-8} \\\Leftrightarrow &3x & = &-1\\\Leftrightarrow & \color{red}{3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+13}& = &8 \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13} & = &8\color{blue}{-13} \\\Leftrightarrow &11x & = &-5\\\Leftrightarrow & \color{red}{11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+8}& = &11 \\\Leftrightarrow & -7x \color{red}{+8}\color{blue}{-8} & = &11\color{blue}{-8} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+14}& = &-2 \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14} & = &-2\color{blue}{-14} \\\Leftrightarrow &-3x & = &-16\\\Leftrightarrow & \color{red}{-3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-11}& = &-1 \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11} & = &-1\color{blue}{+11} \\\Leftrightarrow &-10x & = &10\\\Leftrightarrow & \color{red}{-10}x & = &10\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{10}{-10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)