Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+1}& = &13 \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1} & = &13\color{blue}{-1} \\\Leftrightarrow &-12x & = &12\\\Leftrightarrow & \color{red}{-12}x & = &12\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{12}{-12} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+5}& = &-11 \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5} & = &-11\color{blue}{-5} \\\Leftrightarrow &4x & = &-16\\\Leftrightarrow & \color{red}{4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-16}{4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+14}& = &-10 \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14} & = &-10\color{blue}{-14} \\\Leftrightarrow &10x & = &-24\\\Leftrightarrow & \color{red}{10}x & = &-24\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-24}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+2}& = &15 \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2} & = &15\color{blue}{-2} \\\Leftrightarrow &-11x & = &13\\\Leftrightarrow & \color{red}{-11}x & = &13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+9}& = &13 \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9} & = &13\color{blue}{-9} \\\Leftrightarrow &9x & = &4\\\Leftrightarrow & \color{red}{9}x & = &4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-12}& = &-9 \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12} & = &-9\color{blue}{+12} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+10}& = &-2 \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10} & = &-2\color{blue}{-10} \\\Leftrightarrow &x & = &-12\\\Leftrightarrow & \color{red}{}x & = &-12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -12 \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-10}& = &6 \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10} & = &6\color{blue}{+10} \\\Leftrightarrow &-14x & = &16\\\Leftrightarrow & \color{red}{-14}x & = &16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{-11}& = &-12 \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11} & = &-12\color{blue}{+11} \\\Leftrightarrow &-9x & = &-1\\\Leftrightarrow & \color{red}{-9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-5}& = &-1 \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5} & = &-1\color{blue}{+5} \\\Leftrightarrow &9x & = &4\\\Leftrightarrow & \color{red}{9}x & = &4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+8}& = &14 \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8} & = &14\color{blue}{-8} \\\Leftrightarrow &12x & = &6\\\Leftrightarrow & \color{red}{12}x & = &6\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{6}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+5}& = &-1 \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5} & = &-1\color{blue}{-5} \\\Leftrightarrow &9x & = &-6\\\Leftrightarrow & \color{red}{9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)