Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+1}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1-13x } & = & -10 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & -10 \color{blue}{-1} \\\Leftrightarrow &-5x & = &-11\\\Leftrightarrow & \color{red}{-5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13-x } & = & 7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &-14x & = &20\\\Leftrightarrow & \color{red}{-14}x & = &20\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{20}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+13}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13-x } & = & -2 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -2 \color{blue}{-13} \\\Leftrightarrow &-15x & = &-15\\\Leftrightarrow & \color{red}{-15}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-15}{-15} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-8}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8-x } & = & -3 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & -3 \color{blue}{+8} \\\Leftrightarrow &4x & = &5\\\Leftrightarrow & \color{red}{4}x & = &5\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{5}{4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-1}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-13x } & = & 1 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 1 \color{blue}{+1} \\\Leftrightarrow &-25x & = &2\\\Leftrightarrow & \color{red}{-25}x & = &2\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{2}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{25} } & & \\ & V = \left\{ \frac{-2}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+8}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-x } & = & 13 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 13 \color{blue}{-8} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-1}& = & -6 \color{red}{ +4x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1-4x } & = & -6 \color{red}{ +4x }\color{blue}{+1-4x } \\\Leftrightarrow & -x \color{blue}{-4x } & = & -6 \color{blue}{+1} \\\Leftrightarrow &-5x & = &-5\\\Leftrightarrow & \color{red}{-5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-5}{-5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-11}& = & 15 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-11}\color{blue}{+11+12x } & = & 15 \color{red}{ -12x }\color{blue}{+11+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 15 \color{blue}{+11} \\\Leftrightarrow &17x & = &26\\\Leftrightarrow & \color{red}{17}x & = &26\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{26}{17} \\\Leftrightarrow & \color{green}{ x = \frac{26}{17} } & & \\ & V = \left\{ \frac{26}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-1}& = & -1 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1+11x } & = & -1 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -1 \color{blue}{+1} \\\Leftrightarrow &17x & = &0\\\Leftrightarrow & \color{red}{17}x & = &0\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{0}{17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-3}& = & 4 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3-12x } & = & 4 \color{red}{ +12x }\color{blue}{+3-12x } \\\Leftrightarrow & 7x \color{blue}{-12x } & = & 4 \color{blue}{+3} \\\Leftrightarrow &-5x & = &7\\\Leftrightarrow & \color{red}{-5}x & = &7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+12}& = & -11 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12+11x } & = & -11 \color{red}{ -11x }\color{blue}{-12+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -11 \color{blue}{-12} \\\Leftrightarrow &17x & = &-23\\\Leftrightarrow & \color{red}{17}x & = &-23\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-23}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{17} } & & \\ & V = \left\{ \frac{-23}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+8}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8-x } & = & -15 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -15 \color{blue}{-8} \\\Leftrightarrow &-9x & = &-23\\\Leftrightarrow & \color{red}{-9}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-23}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{23}{9} } & & \\ & V = \left\{ \frac{23}{9} \right\} & \\\end{align}\)