Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-10}& = & -15 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10+3x } & = & -15 \color{red}{ -3x }\color{blue}{+10+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -15 \color{blue}{+10} \\\Leftrightarrow &13x & = &-5\\\Leftrightarrow & \color{red}{13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+10}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10-5x } & = & 8 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 8 \color{blue}{-10} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-5}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5-x } & = & -4 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -4 \color{blue}{+5} \\\Leftrightarrow &-3x & = &1\\\Leftrightarrow & \color{red}{-3}x & = &1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+8}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8-5x } & = & -1 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &3x & = &-9\\\Leftrightarrow & \color{red}{3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-9}{3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-12}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12+11x } & = & -3 \color{red}{ -11x }\color{blue}{+12+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & -3 \color{blue}{+12} \\\Leftrightarrow &25x & = &9\\\Leftrightarrow & \color{red}{25}x & = &9\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{9}{25} \\\Leftrightarrow & \color{green}{ x = \frac{9}{25} } & & \\ & V = \left\{ \frac{9}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-4}& = & 5 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{-4}\color{blue}{+4+9x } & = & 5 \color{red}{ -9x }\color{blue}{+4+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &8x & = &9\\\Leftrightarrow & \color{red}{8}x & = &9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-5}& = & -7 \color{red}{ -3x } \\\Leftrightarrow & 13x \color{red}{-5}\color{blue}{+5+3x } & = & -7 \color{red}{ -3x }\color{blue}{+5+3x } \\\Leftrightarrow & 13x \color{blue}{+3x } & = & -7 \color{blue}{+5} \\\Leftrightarrow &16x & = &-2\\\Leftrightarrow & \color{red}{16}x & = &-2\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-2}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-1}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-1}\color{blue}{+1-x } & = & -10 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -10 \color{blue}{+1} \\\Leftrightarrow &-5x & = &-9\\\Leftrightarrow & \color{red}{-5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+6}& = & 3 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6+10x } & = & 3 \color{red}{ -10x }\color{blue}{-6+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 3 \color{blue}{-6} \\\Leftrightarrow &21x & = &-3\\\Leftrightarrow & \color{red}{21}x & = &-3\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-3}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-2}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2-x } & = & 1 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 1 \color{blue}{+2} \\\Leftrightarrow &-6x & = &3\\\Leftrightarrow & \color{red}{-6}x & = &3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-8}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-8}\color{blue}{+8-7x } & = & -11 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -11 \color{blue}{+8} \\\Leftrightarrow &-13x & = &-3\\\Leftrightarrow & \color{red}{-13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+8}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+8}\color{blue}{-8-x } & = & 10 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 10 \color{blue}{-8} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)