Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+9}& = & 4 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9+9x } & = & 4 \color{red}{ -9x }\color{blue}{-9+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 4 \color{blue}{-9} \\\Leftrightarrow &19x & = &-5\\\Leftrightarrow & \color{red}{19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{19} } & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-14}& = & -3 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-8x } & = & -3 \color{red}{ +8x }\color{blue}{+14-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &-15x & = &11\\\Leftrightarrow & \color{red}{-15}x & = &11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8-x } & = & -14 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-11}& = & -8 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11+13x } & = & -8 \color{red}{ -13x }\color{blue}{+11+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -8 \color{blue}{+11} \\\Leftrightarrow &24x & = &3\\\Leftrightarrow & \color{red}{24}x & = &3\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{3}{24} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+12}& = & -8 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12+15x } & = & -8 \color{red}{ -15x }\color{blue}{-12+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &19x & = &-20\\\Leftrightarrow & \color{red}{19}x & = &-20\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-20}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{19} } & & \\ & V = \left\{ \frac{-20}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+12}& = & 11 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+12}\color{blue}{-12+7x } & = & 11 \color{red}{ -7x }\color{blue}{-12+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &22x & = &-1\\\Leftrightarrow & \color{red}{22}x & = &-1\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-1}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{22} } & & \\ & V = \left\{ \frac{-1}{22} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-8}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-x } & = & -6 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -6 \color{blue}{+8} \\\Leftrightarrow &-8x & = &2\\\Leftrightarrow & \color{red}{-8}x & = &2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14-x } & = & 14 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 14 \color{blue}{+14} \\\Leftrightarrow &-7x & = &28\\\Leftrightarrow & \color{red}{-7}x & = &28\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{28}{-7} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+12}& = & -3 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12+7x } & = & -3 \color{red}{ -7x }\color{blue}{-12+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -3 \color{blue}{-12} \\\Leftrightarrow &15x & = &-15\\\Leftrightarrow & \color{red}{15}x & = &-15\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-15}{15} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+14}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-x } & = & 12 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-2\\\Leftrightarrow & \color{red}{-11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+10}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10-7x } & = & 2 \color{red}{ +7x }\color{blue}{-10-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 2 \color{blue}{-10} \\\Leftrightarrow &-17x & = &-8\\\Leftrightarrow & \color{red}{-17}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{8}{17} } & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{+15}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15-x } & = & -5 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -5 \color{blue}{-15} \\\Leftrightarrow &11x & = &-20\\\Leftrightarrow & \color{red}{11}x & = &-20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)