Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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