Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+4}& = & -10 \color{red}{ +6x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4-6x } & = & -10 \color{red}{ +6x }\color{blue}{-4-6x } \\\Leftrightarrow & 13x \color{blue}{-6x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &7x & = &-14\\\Leftrightarrow & \color{red}{7}x & = &-14\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-14}{7} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+9}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9-x } & = & -13 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -13 \color{blue}{-9} \\\Leftrightarrow &3x & = &-22\\\Leftrightarrow & \color{red}{3}x & = &-22\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-22}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{3} } & & \\ & V = \left\{ \frac{-22}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+6}& = & 7 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-14x } & = & 7 \color{red}{ +14x }\color{blue}{-6-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &-23x & = &1\\\Leftrightarrow & \color{red}{-23}x & = &1\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{1}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+5}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-x } & = & -15 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &-12x & = &-20\\\Leftrightarrow & \color{red}{-12}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-20}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+14}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-x } & = & -6 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -6 \color{blue}{-14} \\\Leftrightarrow &-3x & = &-20\\\Leftrightarrow & \color{red}{-3}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{20}{3} } & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{+15}& = & -7 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{+15}\color{blue}{-15-8x } & = & -7 \color{red}{ +8x }\color{blue}{-15-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &-x & = &-22\\\Leftrightarrow & \color{red}{-}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-22}{-1} \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-9}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{-9}\color{blue}{+9-13x } & = & -10 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 5x \color{blue}{-13x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &-8x & = &-1\\\Leftrightarrow & \color{red}{-8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+12}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12-13x } & = & -10 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -10 \color{blue}{-12} \\\Leftrightarrow &-28x & = &-22\\\Leftrightarrow & \color{red}{-28}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-22}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{11}{14} } & & \\ & V = \left\{ \frac{11}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-15}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-x } & = & -4 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -4 \color{blue}{+15} \\\Leftrightarrow &-8x & = &11\\\Leftrightarrow & \color{red}{-8}x & = &11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2-x } & = & 15 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &-12x & = &13\\\Leftrightarrow & \color{red}{-12}x & = &13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{12} } & & \\ & V = \left\{ \frac{-13}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-6}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-x } & = & -4 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -4 \color{blue}{+6} \\\Leftrightarrow &-13x & = &2\\\Leftrightarrow & \color{red}{-13}x & = &2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+5}& = & 4 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5+4x } & = & 4 \color{red}{ -4x }\color{blue}{-5+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &9x & = &-1\\\Leftrightarrow & \color{red}{9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)