Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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