Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+4}& = &-5 \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4} & = &-5\color{blue}{-4} \\\Leftrightarrow &12x & = &-9\\\Leftrightarrow & \color{red}{12}x & = &-9\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-9}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+1}& = &4 \\\Leftrightarrow & -3x \color{red}{+1}\color{blue}{-1} & = &4\color{blue}{-1} \\\Leftrightarrow &-3x & = &3\\\Leftrightarrow & \color{red}{-3}x & = &3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{3}{-3} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+11}& = &-15 \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11} & = &-15\color{blue}{-11} \\\Leftrightarrow &13x & = &-26\\\Leftrightarrow & \color{red}{13}x & = &-26\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-26}{13} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-4}& = &-9 \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4} & = &-9\color{blue}{+4} \\\Leftrightarrow &3x & = &-5\\\Leftrightarrow & \color{red}{3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-5}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-3}& = &-13 \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3} & = &-13\color{blue}{+3} \\\Leftrightarrow &2x & = &-10\\\Leftrightarrow & \color{red}{2}x & = &-10\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-10}{2} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+14}& = &-3 \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14} & = &-3\color{blue}{-14} \\\Leftrightarrow &8x & = &-17\\\Leftrightarrow & \color{red}{8}x & = &-17\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-17}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{8} } & & \\ & V = \left\{ \frac{-17}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+8}& = &-11 \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8} & = &-11\color{blue}{-8} \\\Leftrightarrow &5x & = &-19\\\Leftrightarrow & \color{red}{5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-19}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{5} } & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+2}& = &8 \\\Leftrightarrow & -13x \color{red}{+2}\color{blue}{-2} & = &8\color{blue}{-2} \\\Leftrightarrow &-13x & = &6\\\Leftrightarrow & \color{red}{-13}x & = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+5}& = &4 \\\Leftrightarrow & -8x \color{red}{+5}\color{blue}{-5} & = &4\color{blue}{-5} \\\Leftrightarrow &-8x & = &-1\\\Leftrightarrow & \color{red}{-8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+12}& = &4 \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12} & = &4\color{blue}{-12} \\\Leftrightarrow &10x & = &-8\\\Leftrightarrow & \color{red}{10}x & = &-8\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-8}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-9}& = &14 \\\Leftrightarrow & -7x \color{red}{-9}\color{blue}{+9} & = &14\color{blue}{+9} \\\Leftrightarrow &-7x & = &23\\\Leftrightarrow & \color{red}{-7}x & = &23\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{23}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{7} } & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-3}& = &-14 \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3} & = &-14\color{blue}{+3} \\\Leftrightarrow &12x & = &-11\\\Leftrightarrow & \color{red}{12}x & = &-11\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-11}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{12} } & & \\ & V = \left\{ \frac{-11}{12} \right\} & \\\end{align}\)