Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{-5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-x } & = & 13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &-5x & = &18\\\Leftrightarrow & \color{red}{-5}x & = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{-9}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & 11 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 11 \color{blue}{+9} \\\Leftrightarrow &-6x & = &20\\\Leftrightarrow & \color{red}{-6}x & = &20\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{20}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+13}& = & -10 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13+9x } & = & -10 \color{red}{ -9x }\color{blue}{-13+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -10 \color{blue}{-13} \\\Leftrightarrow &14x & = &-23\\\Leftrightarrow & \color{red}{14}x & = &-23\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-23}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{14} } & & \\ & V = \left\{ \frac{-23}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+15}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15-x } & = & -3 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & -3 \color{blue}{-15} \\\Leftrightarrow &14x & = &-18\\\Leftrightarrow & \color{red}{14}x & = &-18\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-18}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+2}& = & 14 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2+11x } & = & 14 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 14 \color{blue}{-2} \\\Leftrightarrow &15x & = &12\\\Leftrightarrow & \color{red}{15}x & = &12\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{12}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+10}& = & -12 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10-10x } & = & -12 \color{red}{ +10x }\color{blue}{-10-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & -12 \color{blue}{-10} \\\Leftrightarrow &-7x & = &-22\\\Leftrightarrow & \color{red}{-7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{22}{7} } & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{-7}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7-13x } & = & -4 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -4 \color{blue}{+7} \\\Leftrightarrow &-25x & = &3\\\Leftrightarrow & \color{red}{-25}x & = &3\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{3}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{25} } & & \\ & V = \left\{ \frac{-3}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-15}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & 3x \color{red}{-15}\color{blue}{+15-11x } & = & 10 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & 3x \color{blue}{-11x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &-8x & = &25\\\Leftrightarrow & \color{red}{-8}x & = &25\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{25}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{8} } & & \\ & V = \left\{ \frac{-25}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+10}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10-x } & = & -5 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -5 \color{blue}{-10} \\\Leftrightarrow &8x & = &-15\\\Leftrightarrow & \color{red}{8}x & = &-15\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-15}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+7}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7-x } & = & -10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -10 \color{blue}{-7} \\\Leftrightarrow &-16x & = &-17\\\Leftrightarrow & \color{red}{-16}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-17}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{17}{16} } & & \\ & V = \left\{ \frac{17}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-9}& = & -6 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9+3x } & = & -6 \color{red}{ -3x }\color{blue}{+9+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -6 \color{blue}{+9} \\\Leftrightarrow &7x & = &3\\\Leftrightarrow & \color{red}{7}x & = &3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{+15}& = & 6 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-4x } & = & 6 \color{red}{ +4x }\color{blue}{-15-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 6 \color{blue}{-15} \\\Leftrightarrow &-7x & = &-9\\\Leftrightarrow & \color{red}{-7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)