Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+8}& = & 12 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8+5x } & = & 12 \color{red}{ -5x }\color{blue}{-8+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & 12 \color{blue}{-8} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+6}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{+6}\color{blue}{-6-3x } & = & -3 \color{red}{ +3x }\color{blue}{-6-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &-14x & = &-9\\\Leftrightarrow & \color{red}{-14}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-10}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-x } & = & -2 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -2 \color{blue}{+10} \\\Leftrightarrow &-6x & = &8\\\Leftrightarrow & \color{red}{-6}x & = &8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-4}& = & -5 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4+12x } & = & -5 \color{red}{ -12x }\color{blue}{+4+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &25x & = &-1\\\Leftrightarrow & \color{red}{25}x & = &-1\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-1}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{25} } & & \\ & V = \left\{ \frac{-1}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-x } & = & 15 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &13x & = &13\\\Leftrightarrow & \color{red}{13}x & = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-3}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3-x } & = & -9 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -9 \color{blue}{+3} \\\Leftrightarrow &-8x & = &-6\\\Leftrightarrow & \color{red}{-8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-8}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8-7x } & = & 7 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & 7 \color{blue}{+8} \\\Leftrightarrow &2x & = &15\\\Leftrightarrow & \color{red}{2}x & = &15\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{15}{2} \\\Leftrightarrow & \color{green}{ x = \frac{15}{2} } & & \\ & V = \left\{ \frac{15}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+11}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11-11x } & = & -11 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & -x \color{blue}{-11x } & = & -11 \color{blue}{-11} \\\Leftrightarrow &-12x & = &-22\\\Leftrightarrow & \color{red}{-12}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-22}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+2}& = & 7 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2+13x } & = & 7 \color{red}{ -13x }\color{blue}{-2+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 7 \color{blue}{-2} \\\Leftrightarrow &27x & = &5\\\Leftrightarrow & \color{red}{27}x & = &5\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{5}{27} \\\Leftrightarrow & \color{green}{ x = \frac{5}{27} } & & \\ & V = \left\{ \frac{5}{27} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-14}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-x } & = & -3 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &-15x & = &11\\\Leftrightarrow & \color{red}{-15}x & = &11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+15}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15-x } & = & 8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 8 \color{blue}{-15} \\\Leftrightarrow &-14x & = &-7\\\Leftrightarrow & \color{red}{-14}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-10}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-7x } & = & -3 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -3 \color{blue}{+10} \\\Leftrightarrow &-17x & = &7\\\Leftrightarrow & \color{red}{-17}x & = &7\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{7}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)