Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-9}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9-13x } & = & 11 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & 11 \color{blue}{+9} \\\Leftrightarrow &-5x & = &20\\\Leftrightarrow & \color{red}{-5}x & = &20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{20}{-5} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-6}& = & -10 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6+9x } & = & -10 \color{red}{ -9x }\color{blue}{+6+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & -10 \color{blue}{+6} \\\Leftrightarrow &8x & = &-4\\\Leftrightarrow & \color{red}{8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+11}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11-7x } & = & 2 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &8x & = &-9\\\Leftrightarrow & \color{red}{8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-13}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-x } & = & -13 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -13 \color{blue}{+13} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+2}& = & 6 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2+13x } & = & 6 \color{red}{ -13x }\color{blue}{-2+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &23x & = &4\\\Leftrightarrow & \color{red}{23}x & = &4\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{4}{23} \\\Leftrightarrow & \color{green}{ x = \frac{4}{23} } & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+15}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+15}\color{blue}{-15-x } & = & 11 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 11 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-4\\\Leftrightarrow & \color{red}{-5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{-7}& = & -2 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7+9x } & = & -2 \color{red}{ -9x }\color{blue}{+7+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -2 \color{blue}{+7} \\\Leftrightarrow &19x & = &5\\\Leftrightarrow & \color{red}{19}x & = &5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+1}& = & 4 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+1}\color{blue}{-1+8x } & = & 4 \color{red}{ -8x }\color{blue}{-1+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 4 \color{blue}{-1} \\\Leftrightarrow &11x & = &3\\\Leftrightarrow & \color{red}{11}x & = &3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-7}& = & -12 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7-14x } & = & -12 \color{red}{ +14x }\color{blue}{+7-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & -12 \color{blue}{+7} \\\Leftrightarrow &-25x & = &-5\\\Leftrightarrow & \color{red}{-25}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-5}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+5}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5-14x } & = & -7 \color{red}{ +14x }\color{blue}{-5-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & -7 \color{blue}{-5} \\\Leftrightarrow &x & = &-12\\\Leftrightarrow & \color{red}{}x & = &-12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -12 \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{+11}& = & 9 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11+5x } & = & 9 \color{red}{ -5x }\color{blue}{-11+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 9 \color{blue}{-11} \\\Leftrightarrow &8x & = &-2\\\Leftrightarrow & \color{red}{8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)