Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+7}& = & 2 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-11x } & = & 2 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 2 \color{blue}{-7} \\\Leftrightarrow &-9x & = &-5\\\Leftrightarrow & \color{red}{-9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-13}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-x } & = & -8 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &-12x & = &5\\\Leftrightarrow & \color{red}{-12}x & = &5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+4}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-x } & = & -4 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -4 \color{blue}{-4} \\\Leftrightarrow &-7x & = &-8\\\Leftrightarrow & \color{red}{-7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+9}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+9}\color{blue}{-9-x } & = & 4 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 4 \color{blue}{-9} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+14}& = & 14 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14+9x } & = & 14 \color{red}{ -9x }\color{blue}{-14+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &23x & = &0\\\Leftrightarrow & \color{red}{23}x & = &0\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{0}{23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+12}& = & 7 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12+7x } & = & 7 \color{red}{ -7x }\color{blue}{-12+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & 7 \color{blue}{-12} \\\Leftrightarrow &18x & = &-5\\\Leftrightarrow & \color{red}{18}x & = &-5\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{-5}{18} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{18} } & & \\ & V = \left\{ \frac{-5}{18} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-3}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3-x } & = & -1 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -1 \color{blue}{+3} \\\Leftrightarrow &-8x & = &2\\\Leftrightarrow & \color{red}{-8}x & = &2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+10}& = & -11 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10+4x } & = & -11 \color{red}{ -4x }\color{blue}{-10+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -11 \color{blue}{-10} \\\Leftrightarrow &13x & = &-21\\\Leftrightarrow & \color{red}{13}x & = &-21\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-21}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{13} } & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-8}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8-7x } & = & 3 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & 3 \color{blue}{+8} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+14}& = & -2 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14-4x } & = & -2 \color{red}{ +4x }\color{blue}{-14-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & -2 \color{blue}{-14} \\\Leftrightarrow &-x & = &-16\\\Leftrightarrow & \color{red}{-}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-16}{-1} \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+14}& = & 2 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+14}\color{blue}{-14-14x } & = & 2 \color{red}{ +14x }\color{blue}{-14-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &-25x & = &-12\\\Leftrightarrow & \color{red}{-25}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-12}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{12}{25} } & & \\ & V = \left\{ \frac{12}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+4}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-x } & = & -11 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -11 \color{blue}{-4} \\\Leftrightarrow &-15x & = &-15\\\Leftrightarrow & \color{red}{-15}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-15}{-15} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)