Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{-13}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13-x } & = & 14 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 14 \color{blue}{+13} \\\Leftrightarrow &4x & = &27\\\Leftrightarrow & \color{red}{4}x & = &27\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{27}{4} \\\Leftrightarrow & \color{green}{ x = \frac{27}{4} } & & \\ & V = \left\{ \frac{27}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-13}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13-7x } & = & -8 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &-4x & = &5\\\Leftrightarrow & \color{red}{-4}x & = &5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+7}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7-x } & = & 1 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 1 \color{blue}{-7} \\\Leftrightarrow &13x & = &-6\\\Leftrightarrow & \color{red}{13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+15}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+15}\color{blue}{-15-x } & = & -11 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -11 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-26\\\Leftrightarrow & \color{red}{-5}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-26}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{26}{5} } & & \\ & V = \left\{ \frac{26}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+7}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7-x } & = & 5 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{-7} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+8}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8-11x } & = & -12 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -12 \color{blue}{-8} \\\Leftrightarrow &-5x & = &-20\\\Leftrightarrow & \color{red}{-5}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-20}{-5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+7}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7-x } & = & 6 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 6 \color{blue}{-7} \\\Leftrightarrow &-9x & = &-1\\\Leftrightarrow & \color{red}{-9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-3}& = & -13 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-14x } & = & -13 \color{red}{ +14x }\color{blue}{+3-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -13 \color{blue}{+3} \\\Leftrightarrow &-23x & = &-10\\\Leftrightarrow & \color{red}{-23}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-10}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{10}{23} } & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-2}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{-2}\color{blue}{+2-9x } & = & 13 \color{red}{ +9x }\color{blue}{+2-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & 13 \color{blue}{+2} \\\Leftrightarrow &-11x & = &15\\\Leftrightarrow & \color{red}{-11}x & = &15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{11} } & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-4}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4-x } & = & 6 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 6 \color{blue}{+4} \\\Leftrightarrow &5x & = &10\\\Leftrightarrow & \color{red}{5}x & = &10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{10}{5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{-13}& = & 9 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13-5x } & = & 9 \color{red}{ +5x }\color{blue}{+13-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 9 \color{blue}{+13} \\\Leftrightarrow &7x & = &22\\\Leftrightarrow & \color{red}{7}x & = &22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{22}{7} } & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{+13}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-11x } & = & -6 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -6 \color{blue}{-13} \\\Leftrightarrow &-21x & = &-19\\\Leftrightarrow & \color{red}{-21}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-19}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{19}{21} } & & \\ & V = \left\{ \frac{19}{21} \right\} & \\\end{align}\)