Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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