Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+13}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+13}\color{blue}{-13-x } & = & 15 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+12}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12-x } & = & -4 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -x \color{blue}{-x } & = & -4 \color{blue}{-12} \\\Leftrightarrow &-2x & = &-16\\\Leftrightarrow & \color{red}{-2}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-16}{-2} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+10}& = & -6 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-14x } & = & -6 \color{red}{ +14x }\color{blue}{-10-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -6 \color{blue}{-10} \\\Leftrightarrow &-23x & = &-16\\\Leftrightarrow & \color{red}{-23}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-16}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{16}{23} } & & \\ & V = \left\{ \frac{16}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+4}& = & 3 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-14x } & = & 3 \color{red}{ +14x }\color{blue}{-4-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 3 \color{blue}{-4} \\\Leftrightarrow &-27x & = &-1\\\Leftrightarrow & \color{red}{-27}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-1}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{1}{27} } & & \\ & V = \left\{ \frac{1}{27} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+8}& = & 14 \color{red}{ +12x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8-12x } & = & 14 \color{red}{ +12x }\color{blue}{-8-12x } \\\Leftrightarrow & 5x \color{blue}{-12x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &-7x & = &6\\\Leftrightarrow & \color{red}{-7}x & = &6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+4}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+4}\color{blue}{-4+11x } & = & -10 \color{red}{ -11x }\color{blue}{-4+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &15x & = &-14\\\Leftrightarrow & \color{red}{15}x & = &-14\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-14}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{15} } & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-3}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-3}\color{blue}{+3-x } & = & 3 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 3 \color{blue}{+3} \\\Leftrightarrow &-9x & = &6\\\Leftrightarrow & \color{red}{-9}x & = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-14}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-x } & = & 15 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 15 \color{blue}{+14} \\\Leftrightarrow &-8x & = &29\\\Leftrightarrow & \color{red}{-8}x & = &29\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{29}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{8} } & & \\ & V = \left\{ \frac{-29}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-14}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14-11x } & = & 12 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 12 \color{blue}{+14} \\\Leftrightarrow &-3x & = &26\\\Leftrightarrow & \color{red}{-3}x & = &26\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{26}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{3} } & & \\ & V = \left\{ \frac{-26}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-3}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-11x } & = & -1 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -1 \color{blue}{+3} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+4}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4-13x } & = & 1 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 1 \color{blue}{-4} \\\Leftrightarrow &-28x & = &-3\\\Leftrightarrow & \color{red}{-28}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-3}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{3}{28} } & & \\ & V = \left\{ \frac{3}{28} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-3}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-x } & = & 10 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &x & = &13\\\Leftrightarrow & \color{red}{}x & = &13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 13 \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)