Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-15}& = & -2 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15+9x } & = & -2 \color{red}{ -9x }\color{blue}{+15+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &23x & = &13\\\Leftrightarrow & \color{red}{23}x & = &13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{13}{23} } & & \\ & V = \left\{ \frac{13}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-13}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-7x } & = & -7 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -7 \color{blue}{+13} \\\Leftrightarrow &-13x & = &6\\\Leftrightarrow & \color{red}{-13}x & = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-10}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-x } & = & -7 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{+15}& = & 7 \color{red}{ +14x } \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15-14x } & = & 7 \color{red}{ +14x }\color{blue}{-15-14x } \\\Leftrightarrow & 9x \color{blue}{-14x } & = & 7 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-8\\\Leftrightarrow & \color{red}{-5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-12}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-13x } & = & -3 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -3 \color{blue}{+12} \\\Leftrightarrow &-28x & = &9\\\Leftrightarrow & \color{red}{-28}x & = &9\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{9}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{28} } & & \\ & V = \left\{ \frac{-9}{28} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+15}& = & -13 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+15}\color{blue}{-15+8x } & = & -13 \color{red}{ -8x }\color{blue}{-15+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &11x & = &-28\\\Leftrightarrow & \color{red}{11}x & = &-28\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-28}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{11} } & & \\ & V = \left\{ \frac{-28}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+4}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & 4 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 4 \color{blue}{-4} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-2}& = & 11 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2+5x } & = & 11 \color{red}{ -5x }\color{blue}{+2+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & 11 \color{blue}{+2} \\\Leftrightarrow &13x & = &13\\\Leftrightarrow & \color{red}{13}x & = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-7}& = & -1 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-7}\color{blue}{+7+11x } & = & -1 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -1 \color{blue}{+7} \\\Leftrightarrow &15x & = &6\\\Leftrightarrow & \color{red}{15}x & = &6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-1}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1-11x } & = & -6 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -6 \color{blue}{+1} \\\Leftrightarrow &-16x & = &-5\\\Leftrightarrow & \color{red}{-16}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{16} } & & \\ & V = \left\{ \frac{5}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-13}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-13x } & = & -1 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -1 \color{blue}{+13} \\\Leftrightarrow &-19x & = &12\\\Leftrightarrow & \color{red}{-19}x & = &12\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{12}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{19} } & & \\ & V = \left\{ \frac{-12}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+11}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+11}\color{blue}{-11-13x } & = & 11 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & 11 \color{blue}{-11} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)