Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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