Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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