Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+13}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13-5x } & = & -11 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & -11 \color{blue}{-13} \\\Leftrightarrow &8x & = &-24\\\Leftrightarrow & \color{red}{8}x & = &-24\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-24}{8} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-12}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-13x } & = & 2 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &-25x & = &14\\\Leftrightarrow & \color{red}{-25}x & = &14\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{14}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{25} } & & \\ & V = \left\{ \frac{-14}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-7}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-7x } & = & -3 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &-20x & = &4\\\Leftrightarrow & \color{red}{-20}x & = &4\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{4}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+2}& = & 11 \color{red}{ +10x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2-10x } & = & 11 \color{red}{ +10x }\color{blue}{-2-10x } \\\Leftrightarrow & 11x \color{blue}{-10x } & = & 11 \color{blue}{-2} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+15}& = & 6 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-6x } & = & 6 \color{red}{ +6x }\color{blue}{-15-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 6 \color{blue}{-15} \\\Leftrightarrow &-17x & = &-9\\\Leftrightarrow & \color{red}{-17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{+11}& = & 6 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11-8x } & = & 6 \color{red}{ +8x }\color{blue}{-11-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 6 \color{blue}{-11} \\\Leftrightarrow &-x & = &-5\\\Leftrightarrow & \color{red}{-}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-5}{-1} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-11}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11-3x } & = & 11 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & 11 \color{blue}{+11} \\\Leftrightarrow &11x & = &22\\\Leftrightarrow & \color{red}{11}x & = &22\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{22}{11} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-7}& = & 9 \color{red}{ +3x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7-3x } & = & 9 \color{red}{ +3x }\color{blue}{+7-3x } \\\Leftrightarrow & 11x \color{blue}{-3x } & = & 9 \color{blue}{+7} \\\Leftrightarrow &8x & = &16\\\Leftrightarrow & \color{red}{8}x & = &16\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{16}{8} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-9}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & -8 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &-6x & = &1\\\Leftrightarrow & \color{red}{-6}x & = &1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+8}& = & -9 \color{red}{ -4x } \\\Leftrightarrow & x \color{red}{+8}\color{blue}{-8+4x } & = & -9 \color{red}{ -4x }\color{blue}{-8+4x } \\\Leftrightarrow & x \color{blue}{+4x } & = & -9 \color{blue}{-8} \\\Leftrightarrow &5x & = &-17\\\Leftrightarrow & \color{red}{5}x & = &-17\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-17}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{5} } & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-5}& = & 12 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{-5}\color{blue}{+5-10x } & = & 12 \color{red}{ +10x }\color{blue}{+5-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &-7x & = &17\\\Leftrightarrow & \color{red}{-7}x & = &17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-1}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-1}\color{blue}{+1-x } & = & 8 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 8 \color{blue}{+1} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)