Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-1}& = &-6 \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1} & = &-6\color{blue}{+1} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+3}& = &-13 \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3} & = &-13\color{blue}{-3} \\\Leftrightarrow &3x & = &-16\\\Leftrightarrow & \color{red}{3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+10}& = &7 \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10} & = &7\color{blue}{-10} \\\Leftrightarrow &5x & = &-3\\\Leftrightarrow & \color{red}{5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-9}& = &2 \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9} & = &2\color{blue}{+9} \\\Leftrightarrow &-6x & = &11\\\Leftrightarrow & \color{red}{-6}x & = &11\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{11}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-5}& = &10 \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5} & = &10\color{blue}{+5} \\\Leftrightarrow &8x & = &15\\\Leftrightarrow & \color{red}{8}x & = &15\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{15}{8} \\\Leftrightarrow & \color{green}{ x = \frac{15}{8} } & & \\ & V = \left\{ \frac{15}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+12}& = &-4 \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12} & = &-4\color{blue}{-12} \\\Leftrightarrow &-10x & = &-16\\\Leftrightarrow & \color{red}{-10}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-16}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-5}& = &-13 \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5} & = &-13\color{blue}{+5} \\\Leftrightarrow &-2x & = &-8\\\Leftrightarrow & \color{red}{-2}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-8}{-2} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-7}& = &3 \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7} & = &3\color{blue}{+7} \\\Leftrightarrow &-7x & = &10\\\Leftrightarrow & \color{red}{-7}x & = &10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+4}& = &9 \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4} & = &9\color{blue}{-4} \\\Leftrightarrow &-6x & = &5\\\Leftrightarrow & \color{red}{-6}x & = &5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+9}& = &-8 \\\Leftrightarrow & 5x \color{red}{+9}\color{blue}{-9} & = &-8\color{blue}{-9} \\\Leftrightarrow &5x & = &-17\\\Leftrightarrow & \color{red}{5}x & = &-17\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-17}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{5} } & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-1}& = &15 \\\Leftrightarrow & -4x \color{red}{-1}\color{blue}{+1} & = &15\color{blue}{+1} \\\Leftrightarrow &-4x & = &16\\\Leftrightarrow & \color{red}{-4}x & = &16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{16}{-4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+7}& = &9 \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7} & = &9\color{blue}{-7} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)