Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-11}& = &-3 \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11} & = &-3\color{blue}{+11} \\\Leftrightarrow &15x & = &8\\\Leftrightarrow & \color{red}{15}x & = &8\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{8}{15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-12}& = &13 \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12} & = &13\color{blue}{+12} \\\Leftrightarrow &3x & = &25\\\Leftrightarrow & \color{red}{3}x & = &25\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{25}{3} \\\Leftrightarrow & \color{green}{ x = \frac{25}{3} } & & \\ & V = \left\{ \frac{25}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-2}& = &-9 \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2} & = &-9\color{blue}{+2} \\\Leftrightarrow &4x & = &-7\\\Leftrightarrow & \color{red}{4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-7}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+4}& = &14 \\\Leftrightarrow & 5x \color{red}{+4}\color{blue}{-4} & = &14\color{blue}{-4} \\\Leftrightarrow &5x & = &10\\\Leftrightarrow & \color{red}{5}x & = &10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{10}{5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+1}& = &-1 \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1} & = &-1\color{blue}{-1} \\\Leftrightarrow &8x & = &-2\\\Leftrightarrow & \color{red}{8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+14}& = &-5 \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14} & = &-5\color{blue}{-14} \\\Leftrightarrow &3x & = &-19\\\Leftrightarrow & \color{red}{3}x & = &-19\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-19}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{3} } & & \\ & V = \left\{ \frac{-19}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+1}& = &-5 \\\Leftrightarrow & -2x \color{red}{+1}\color{blue}{-1} & = &-5\color{blue}{-1} \\\Leftrightarrow &-2x & = &-6\\\Leftrightarrow & \color{red}{-2}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-6}{-2} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-13}& = &9 \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13} & = &9\color{blue}{+13} \\\Leftrightarrow &-6x & = &22\\\Leftrightarrow & \color{red}{-6}x & = &22\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{22}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-15}& = &-3 \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15} & = &-3\color{blue}{+15} \\\Leftrightarrow &-10x & = &12\\\Leftrightarrow & \color{red}{-10}x & = &12\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{12}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-10}& = &2 \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10} & = &2\color{blue}{+10} \\\Leftrightarrow &9x & = &12\\\Leftrightarrow & \color{red}{9}x & = &12\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{12}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-11}& = &2 \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11} & = &2\color{blue}{+11} \\\Leftrightarrow &3x & = &13\\\Leftrightarrow & \color{red}{3}x & = &13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+8}& = &-8 \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8} & = &-8\color{blue}{-8} \\\Leftrightarrow &13x & = &-16\\\Leftrightarrow & \color{red}{13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)