Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-10}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10-x } & = & 14 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 14 \color{blue}{+10} \\\Leftrightarrow &x & = &24\\\Leftrightarrow & \color{red}{}x & = &24\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 24 \\\Leftrightarrow & \color{green}{ x = 24 } & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+15}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15-13x } & = & -7 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &-28x & = &-22\\\Leftrightarrow & \color{red}{-28}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-22}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{11}{14} } & & \\ & V = \left\{ \frac{11}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15-x } & = & -14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &-11x & = &-29\\\Leftrightarrow & \color{red}{-11}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-29}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{29}{11} } & & \\ & V = \left\{ \frac{29}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-2}& = & 5 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2+3x } & = & 5 \color{red}{ -3x }\color{blue}{+2+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 5 \color{blue}{+2} \\\Leftrightarrow &10x & = &7\\\Leftrightarrow & \color{red}{10}x & = &7\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{7}{10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-3}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3+11x } & = & 1 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 1 \color{blue}{+3} \\\Leftrightarrow &20x & = &4\\\Leftrightarrow & \color{red}{20}x & = &4\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{4}{20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+10}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-x } & = & -11 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -11 \color{blue}{-10} \\\Leftrightarrow &-6x & = &-21\\\Leftrightarrow & \color{red}{-6}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-21}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11-x } & = & 13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+1}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+1}\color{blue}{-1-x } & = & -10 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -10 \color{blue}{-1} \\\Leftrightarrow &-3x & = &-11\\\Leftrightarrow & \color{red}{-3}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-11}& = & 7 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-11}\color{blue}{+11+5x } & = & 7 \color{red}{ -5x }\color{blue}{+11+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &11x & = &18\\\Leftrightarrow & \color{red}{11}x & = &18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+13}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+13}\color{blue}{-13-x } & = & -2 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -2 \color{blue}{-13} \\\Leftrightarrow &-14x & = &-15\\\Leftrightarrow & \color{red}{-14}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{15}{14} } & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-9}& = & 4 \color{red}{ +3x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9-3x } & = & 4 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & x \color{blue}{-3x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &-2x & = &13\\\Leftrightarrow & \color{red}{-2}x & = &13\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{13}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{2} } & & \\ & V = \left\{ \frac{-13}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+6}& = & -1 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+6}\color{blue}{-6+5x } & = & -1 \color{red}{ -5x }\color{blue}{-6+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -1 \color{blue}{-6} \\\Leftrightarrow &11x & = &-7\\\Leftrightarrow & \color{red}{11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)