Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+3}& = & -15 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+3}\color{blue}{-3+6x } & = & -15 \color{red}{ -6x }\color{blue}{-3+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -15 \color{blue}{-3} \\\Leftrightarrow &19x & = &-18\\\Leftrightarrow & \color{red}{19}x & = &-18\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-18}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{19} } & & \\ & V = \left\{ \frac{-18}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+12}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12-9x } & = & -10 \color{red}{ +9x }\color{blue}{-12-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & -10 \color{blue}{-12} \\\Leftrightarrow &x & = &-22\\\Leftrightarrow & \color{red}{}x & = &-22\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -22 \\\Leftrightarrow & \color{green}{ x = -22 } & & \\ & V = \left\{ -22 \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+11}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11-x } & = & 2 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &-6x & = &-9\\\Leftrightarrow & \color{red}{-6}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+12}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12+13x } & = & 8 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 8 \color{blue}{-12} \\\Leftrightarrow &23x & = &-4\\\Leftrightarrow & \color{red}{23}x & = &-4\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-4}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{23} } & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-12}& = & 1 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12+4x } & = & 1 \color{red}{ -4x }\color{blue}{+12+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 1 \color{blue}{+12} \\\Leftrightarrow &13x & = &13\\\Leftrightarrow & \color{red}{13}x & = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{+13}& = & -5 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{+13}\color{blue}{-13+9x } & = & -5 \color{red}{ -9x }\color{blue}{-13+9x } \\\Leftrightarrow & 7x \color{blue}{+9x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &16x & = &-18\\\Leftrightarrow & \color{red}{16}x & = &-18\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-18}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-8}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-x } & = & -1 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -1 \color{blue}{+8} \\\Leftrightarrow &-14x & = &7\\\Leftrightarrow & \color{red}{-14}x & = &7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15-x } & = & 12 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 12 \color{blue}{-15} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-8}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8-x } & = & -6 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -6 \color{blue}{+8} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-14}& = & 1 \color{red}{ +2x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14-2x } & = & 1 \color{red}{ +2x }\color{blue}{+14-2x } \\\Leftrightarrow & 13x \color{blue}{-2x } & = & 1 \color{blue}{+14} \\\Leftrightarrow &11x & = &15\\\Leftrightarrow & \color{red}{11}x & = &15\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{15}{11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+4}& = & -13 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{+4}\color{blue}{-4-8x } & = & -13 \color{red}{ +8x }\color{blue}{-4-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & -13 \color{blue}{-4} \\\Leftrightarrow &-3x & = &-17\\\Leftrightarrow & \color{red}{-3}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-17}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{17}{3} } & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+15}& = & -12 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15+6x } & = & -12 \color{red}{ -6x }\color{blue}{-15+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -12 \color{blue}{-15} \\\Leftrightarrow &19x & = &-27\\\Leftrightarrow & \color{red}{19}x & = &-27\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-27}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{19} } & & \\ & V = \left\{ \frac{-27}{19} \right\} & \\\end{align}\)