Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-14}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14+13x } & = & -3 \color{red}{ -13x }\color{blue}{+14+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &23x & = &11\\\Leftrightarrow & \color{red}{23}x & = &11\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{11}{23} \\\Leftrightarrow & \color{green}{ x = \frac{11}{23} } & & \\ & V = \left\{ \frac{11}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+1}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+1}\color{blue}{-1-7x } & = & -10 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -10 \color{blue}{-1} \\\Leftrightarrow &-20x & = &-11\\\Leftrightarrow & \color{red}{-20}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-11}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{11}{20} } & & \\ & V = \left\{ \frac{11}{20} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-6}& = & -4 \color{red}{ -6x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6+6x } & = & -4 \color{red}{ -6x }\color{blue}{+6+6x } \\\Leftrightarrow & x \color{blue}{+6x } & = & -4 \color{blue}{+6} \\\Leftrightarrow &7x & = &2\\\Leftrightarrow & \color{red}{7}x & = &2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+14}& = & -3 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14+10x } & = & -3 \color{red}{ -10x }\color{blue}{-14+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &21x & = &-17\\\Leftrightarrow & \color{red}{21}x & = &-17\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-17}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{21} } & & \\ & V = \left\{ \frac{-17}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-13}& = & -6 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13-10x } & = & -6 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -6 \color{blue}{+13} \\\Leftrightarrow &-19x & = &7\\\Leftrightarrow & \color{red}{-19}x & = &7\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{7}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{19} } & & \\ & V = \left\{ \frac{-7}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-10}& = & 10 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10-9x } & = & 10 \color{red}{ +9x }\color{blue}{+10-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 10 \color{blue}{+10} \\\Leftrightarrow &-17x & = &20\\\Leftrightarrow & \color{red}{-17}x & = &20\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{20}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{17} } & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+4}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+4}\color{blue}{-4-x } & = & -10 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &-4x & = &-14\\\Leftrightarrow & \color{red}{-4}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-14}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+4}& = & 3 \color{red}{ -6x } \\\Leftrightarrow & x \color{red}{+4}\color{blue}{-4+6x } & = & 3 \color{red}{ -6x }\color{blue}{-4+6x } \\\Leftrightarrow & x \color{blue}{+6x } & = & 3 \color{blue}{-4} \\\Leftrightarrow &7x & = &-1\\\Leftrightarrow & \color{red}{7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-2}& = & -4 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-11x } & = & -4 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -4 \color{blue}{+2} \\\Leftrightarrow &-21x & = &-2\\\Leftrightarrow & \color{red}{-21}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-2}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{2}{21} } & & \\ & V = \left\{ \frac{2}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+15}& = & 10 \color{red}{ +10x } \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15-10x } & = & 10 \color{red}{ +10x }\color{blue}{-15-10x } \\\Leftrightarrow & -13x \color{blue}{-10x } & = & 10 \color{blue}{-15} \\\Leftrightarrow &-23x & = &-5\\\Leftrightarrow & \color{red}{-23}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-5}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{5}{23} } & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+12}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12-13x } & = & -8 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &-28x & = &-20\\\Leftrightarrow & \color{red}{-28}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-20}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{-4}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4-x } & = & 8 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &-3x & = &12\\\Leftrightarrow & \color{red}{-3}x & = &12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{12}{-3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)