Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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