Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+13}& = &-5 \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13} & = &-5\color{blue}{-13} \\\Leftrightarrow &-10x & = &-18\\\Leftrightarrow & \color{red}{-10}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-18}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+3}& = &1 \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3} & = &1\color{blue}{-3} \\\Leftrightarrow &12x & = &-2\\\Leftrightarrow & \color{red}{12}x & = &-2\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-2}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-9}& = &3 \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9} & = &3\color{blue}{+9} \\\Leftrightarrow &-9x & = &12\\\Leftrightarrow & \color{red}{-9}x & = &12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-7}& = &5 \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7} & = &5\color{blue}{+7} \\\Leftrightarrow &7x & = &12\\\Leftrightarrow & \color{red}{7}x & = &12\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{12}{7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-4}& = &6 \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4} & = &6\color{blue}{+4} \\\Leftrightarrow &-12x & = &10\\\Leftrightarrow & \color{red}{-12}x & = &10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-1}& = &-10 \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1} & = &-10\color{blue}{+1} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-15}& = &4 \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15} & = &4\color{blue}{+15} \\\Leftrightarrow &2x & = &19\\\Leftrightarrow & \color{red}{2}x & = &19\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{19}{2} \\\Leftrightarrow & \color{green}{ x = \frac{19}{2} } & & \\ & V = \left\{ \frac{19}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+10}& = &12 \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10} & = &12\color{blue}{-10} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+6}& = &-4 \\\Leftrightarrow & -11x \color{red}{+6}\color{blue}{-6} & = &-4\color{blue}{-6} \\\Leftrightarrow &-11x & = &-10\\\Leftrightarrow & \color{red}{-11}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-11}& = &13 \\\Leftrightarrow & -12x \color{red}{-11}\color{blue}{+11} & = &13\color{blue}{+11} \\\Leftrightarrow &-12x & = &24\\\Leftrightarrow & \color{red}{-12}x & = &24\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{24}{-12} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-8}& = &-13 \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8} & = &-13\color{blue}{+8} \\\Leftrightarrow &4x & = &-5\\\Leftrightarrow & \color{red}{4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-5}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+11}& = &-15 \\\Leftrightarrow & -4x \color{red}{+11}\color{blue}{-11} & = &-15\color{blue}{-11} \\\Leftrightarrow &-4x & = &-26\\\Leftrightarrow & \color{red}{-4}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-26}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{2} } & & \\ & V = \left\{ \frac{13}{2} \right\} & \\\end{align}\)