Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-4}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4+11x } & = & 9 \color{red}{ -11x }\color{blue}{+4+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 9 \color{blue}{+4} \\\Leftrightarrow &17x & = &13\\\Leftrightarrow & \color{red}{17}x & = &13\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{13}{17} \\\Leftrightarrow & \color{green}{ x = \frac{13}{17} } & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+7}& = & 14 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7-9x } & = & 14 \color{red}{ +9x }\color{blue}{-7-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 14 \color{blue}{-7} \\\Leftrightarrow &5x & = &7\\\Leftrightarrow & \color{red}{5}x & = &7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+8}& = & 5 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-4x } & = & 5 \color{red}{ +4x }\color{blue}{-8-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &-7x & = &-3\\\Leftrightarrow & \color{red}{-7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-8}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-8}\color{blue}{+8-x } & = & -12 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -12 \color{blue}{+8} \\\Leftrightarrow &-7x & = &-4\\\Leftrightarrow & \color{red}{-7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+11}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+11}\color{blue}{-11-x } & = & -4 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -4 \color{blue}{-11} \\\Leftrightarrow &-4x & = &-15\\\Leftrightarrow & \color{red}{-4}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-15}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{15}{4} } & & \\ & V = \left\{ \frac{15}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-11}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11-x } & = & -5 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -5 \color{blue}{+11} \\\Leftrightarrow &-10x & = &6\\\Leftrightarrow & \color{red}{-10}x & = &6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-12}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12+7x } & = & -4 \color{red}{ -7x }\color{blue}{+12+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &11x & = &8\\\Leftrightarrow & \color{red}{11}x & = &8\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{8}{11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-3}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3-x } & = & -6 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -6 \color{blue}{+3} \\\Leftrightarrow &-5x & = &-3\\\Leftrightarrow & \color{red}{-5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+6}& = & 8 \color{red}{ +11x } \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6-11x } & = & 8 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & 13x \color{blue}{-11x } & = & 8 \color{blue}{-6} \\\Leftrightarrow &2x & = &2\\\Leftrightarrow & \color{red}{2}x & = &2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{2}{2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-14}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14+13x } & = & -5 \color{red}{ -13x }\color{blue}{+14+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -5 \color{blue}{+14} \\\Leftrightarrow &27x & = &9\\\Leftrightarrow & \color{red}{27}x & = &9\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{9}{27} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{-9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-x } & = & -9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -9 \color{blue}{+9} \\\Leftrightarrow &-10x & = &0\\\Leftrightarrow & \color{red}{-10}x & = &0\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{0}{-10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+8}& = & -9 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+8}\color{blue}{-8-8x } & = & -9 \color{red}{ +8x }\color{blue}{-8-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -9 \color{blue}{-8} \\\Leftrightarrow &-15x & = &-17\\\Leftrightarrow & \color{red}{-15}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{17}{15} } & & \\ & V = \left\{ \frac{17}{15} \right\} & \\\end{align}\)