Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-9}& = & -6 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9+7x } & = & -6 \color{red}{ -7x }\color{blue}{+9+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -6 \color{blue}{+9} \\\Leftrightarrow &22x & = &3\\\Leftrightarrow & \color{red}{22}x & = &3\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{3}{22} \\\Leftrightarrow & \color{green}{ x = \frac{3}{22} } & & \\ & V = \left\{ \frac{3}{22} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+5}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-x } & = & -11 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -11 \color{blue}{-5} \\\Leftrightarrow &-7x & = &-16\\\Leftrightarrow & \color{red}{-7}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{16}{7} } & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-7}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-7}\color{blue}{+7-9x } & = & -7 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &-17x & = &0\\\Leftrightarrow & \color{red}{-17}x & = &0\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{0}{-17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-4}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-7x } & = & -1 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -1 \color{blue}{+4} \\\Leftrightarrow &-17x & = &3\\\Leftrightarrow & \color{red}{-17}x & = &3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-7}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7-5x } & = & 7 \color{red}{ +5x }\color{blue}{+7-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 7 \color{blue}{+7} \\\Leftrightarrow &-17x & = &14\\\Leftrightarrow & \color{red}{-17}x & = &14\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{14}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{17} } & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-15}& = & 12 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{-15}\color{blue}{+15-8x } & = & 12 \color{red}{ +8x }\color{blue}{+15-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & 12 \color{blue}{+15} \\\Leftrightarrow &-3x & = &27\\\Leftrightarrow & \color{red}{-3}x & = &27\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{27}{-3} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-4}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4-x } & = & 3 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 3 \color{blue}{+4} \\\Leftrightarrow &-5x & = &7\\\Leftrightarrow & \color{red}{-5}x & = &7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-12}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{-12}\color{blue}{+12-13x } & = & -9 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & -9 \color{blue}{+12} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+9}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9-5x } & = & -15 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &-9x & = &-24\\\Leftrightarrow & \color{red}{-9}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-24}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-13}& = & 4 \color{red}{ +4x } \\\Leftrightarrow & 13x \color{red}{-13}\color{blue}{+13-4x } & = & 4 \color{red}{ +4x }\color{blue}{+13-4x } \\\Leftrightarrow & 13x \color{blue}{-4x } & = & 4 \color{blue}{+13} \\\Leftrightarrow &9x & = &17\\\Leftrightarrow & \color{red}{9}x & = &17\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{17}{9} \\\Leftrightarrow & \color{green}{ x = \frac{17}{9} } & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-8}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8-11x } & = & 11 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & 14x \color{blue}{-11x } & = & 11 \color{blue}{+8} \\\Leftrightarrow &3x & = &19\\\Leftrightarrow & \color{red}{3}x & = &19\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{19}{3} \\\Leftrightarrow & \color{green}{ x = \frac{19}{3} } & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-10}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10-x } & = & -11 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -11 \color{blue}{+10} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)