Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-14}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14-7x } & = & 15 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 15 \color{blue}{+14} \\\Leftrightarrow &-10x & = &29\\\Leftrightarrow & \color{red}{-10}x & = &29\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{29}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{10} } & & \\ & V = \left\{ \frac{-29}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-11}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-11}\color{blue}{+11-x } & = & 4 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 4 \color{blue}{+11} \\\Leftrightarrow &-14x & = &15\\\Leftrightarrow & \color{red}{-14}x & = &15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{14} } & & \\ & V = \left\{ \frac{-15}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3-x } & = & -12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &5x & = &-15\\\Leftrightarrow & \color{red}{5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-15}{5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+1}& = & 5 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1-7x } & = & 5 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 5 \color{blue}{-1} \\\Leftrightarrow &-17x & = &4\\\Leftrightarrow & \color{red}{-17}x & = &4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-1}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & 3 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-15}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{-15}\color{blue}{+15-11x } & = & -9 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & -9 \color{blue}{+15} \\\Leftrightarrow &-6x & = &6\\\Leftrightarrow & \color{red}{-6}x & = &6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{6}{-6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+6}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-x } & = & 7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+5}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5-x } & = & -15 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &-16x & = &-20\\\Leftrightarrow & \color{red}{-16}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-20}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+1}& = & -6 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1-5x } & = & -6 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &3x & = &-7\\\Leftrightarrow & \color{red}{3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-7}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+9}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9-x } & = & -8 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -8 \color{blue}{-9} \\\Leftrightarrow &13x & = &-17\\\Leftrightarrow & \color{red}{13}x & = &-17\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-17}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-2}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2-7x } & = & -12 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -12 \color{blue}{+2} \\\Leftrightarrow &3x & = &-10\\\Leftrightarrow & \color{red}{3}x & = &-10\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-10}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+3}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-x } & = & 11 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 11 \color{blue}{-3} \\\Leftrightarrow &-14x & = &8\\\Leftrightarrow & \color{red}{-14}x & = &8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)