Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-2}& = & -4 \color{red}{ +11x } \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2-11x } & = & -4 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & 3x \color{blue}{-11x } & = & -4 \color{blue}{+2} \\\Leftrightarrow &-8x & = &-2\\\Leftrightarrow & \color{red}{-8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-4}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-4}\color{blue}{+4-x } & = & 11 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &-8x & = &15\\\Leftrightarrow & \color{red}{-8}x & = &15\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{15}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-9}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9-x } & = & 10 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &-15x & = &19\\\Leftrightarrow & \color{red}{-15}x & = &19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{15} } & & \\ & V = \left\{ \frac{-19}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+15}& = & 13 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+15}\color{blue}{-15+8x } & = & 13 \color{red}{ -8x }\color{blue}{-15+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 13 \color{blue}{-15} \\\Leftrightarrow &11x & = &-2\\\Leftrightarrow & \color{red}{11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-1}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1-11x } & = & 7 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 7 \color{blue}{+1} \\\Leftrightarrow &-16x & = &8\\\Leftrightarrow & \color{red}{-16}x & = &8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+1}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+1}\color{blue}{-1-x } & = & 13 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &-14x & = &12\\\Leftrightarrow & \color{red}{-14}x & = &12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+3}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3+7x } & = & -4 \color{red}{ -7x }\color{blue}{-3+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &15x & = &-7\\\Leftrightarrow & \color{red}{15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+5}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5-x } & = & 7 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 7 \color{blue}{-5} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+12}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12-x } & = & -14 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -14 \color{blue}{-12} \\\Leftrightarrow &-6x & = &-26\\\Leftrightarrow & \color{red}{-6}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-26}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+4}& = & 12 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4+3x } & = & 12 \color{red}{ -3x }\color{blue}{-4+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &10x & = &8\\\Leftrightarrow & \color{red}{10}x & = &8\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{8}{10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+13}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-x } & = & -4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -4 \color{blue}{-13} \\\Leftrightarrow &-6x & = &-17\\\Leftrightarrow & \color{red}{-6}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{17}{6} } & & \\ & V = \left\{ \frac{17}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-13}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13-x } & = & 15 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 15 \color{blue}{+13} \\\Leftrightarrow &-14x & = &28\\\Leftrightarrow & \color{red}{-14}x & = &28\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{28}{-14} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)