Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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