Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+8}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8-13x } & = & -5 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & -5 \color{blue}{-8} \\\Leftrightarrow &-7x & = &-13\\\Leftrightarrow & \color{red}{-7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3-x } & = & -11 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -11 \color{blue}{-3} \\\Leftrightarrow &8x & = &-14\\\Leftrightarrow & \color{red}{8}x & = &-14\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-14}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+15}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15-x } & = & -8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &9x & = &-23\\\Leftrightarrow & \color{red}{9}x & = &-23\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-23}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{9} } & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+13}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+13}\color{blue}{-13-7x } & = & 2 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 2 \color{blue}{-13} \\\Leftrightarrow &-20x & = &-11\\\Leftrightarrow & \color{red}{-20}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-11}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{11}{20} } & & \\ & V = \left\{ \frac{11}{20} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-9}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-11x } & = & -3 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -3 \color{blue}{+9} \\\Leftrightarrow &-16x & = &6\\\Leftrightarrow & \color{red}{-16}x & = &6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+14}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14-13x } & = & -11 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & -11 \color{blue}{-14} \\\Leftrightarrow &-2x & = &-25\\\Leftrightarrow & \color{red}{-2}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-25}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{25}{2} } & & \\ & V = \left\{ \frac{25}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-13}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-11x } & = & 15 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 15 \color{blue}{+13} \\\Leftrightarrow &-18x & = &28\\\Leftrightarrow & \color{red}{-18}x & = &28\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{28}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{-12}& = & -7 \color{red}{ -12x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12+12x } & = & -7 \color{red}{ -12x }\color{blue}{+12+12x } \\\Leftrightarrow & -x \color{blue}{+12x } & = & -7 \color{blue}{+12} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-15}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15-x } & = & 15 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 15 \color{blue}{+15} \\\Leftrightarrow &x & = &30\\\Leftrightarrow & \color{red}{}x & = &30\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 30 \\\Leftrightarrow & \color{green}{ x = 30 } & & \\ & V = \left\{ 30 \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-3}& = & 10 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-14x } & = & 10 \color{red}{ +14x }\color{blue}{+3-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &-27x & = &13\\\Leftrightarrow & \color{red}{-27}x & = &13\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{13}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{27} } & & \\ & V = \left\{ \frac{-13}{27} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+4}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-x } & = & -12 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -12 \color{blue}{-4} \\\Leftrightarrow &-3x & = &-16\\\Leftrightarrow & \color{red}{-3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-15}& = & 6 \color{red}{ -7x } \\\Leftrightarrow & x \color{red}{-15}\color{blue}{+15+7x } & = & 6 \color{red}{ -7x }\color{blue}{+15+7x } \\\Leftrightarrow & x \color{blue}{+7x } & = & 6 \color{blue}{+15} \\\Leftrightarrow &8x & = &21\\\Leftrightarrow & \color{red}{8}x & = &21\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{21}{8} \\\Leftrightarrow & \color{green}{ x = \frac{21}{8} } & & \\ & V = \left\{ \frac{21}{8} \right\} & \\\end{align}\)