Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+7}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-5x } & = & 7 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 7 \color{blue}{-7} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+6}\color{blue}{-6-x } & = & -3 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &-12x & = &-9\\\Leftrightarrow & \color{red}{-12}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-9}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-3}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-11x } & = & 14 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &-21x & = &17\\\Leftrightarrow & \color{red}{-21}x & = &17\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{17}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{21} } & & \\ & V = \left\{ \frac{-17}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+1}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1-13x } & = & -14 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & -14 \color{blue}{-1} \\\Leftrightarrow &-9x & = &-15\\\Leftrightarrow & \color{red}{-9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+3}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3-x } & = & -7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -7 \color{blue}{-3} \\\Leftrightarrow &-9x & = &-10\\\Leftrightarrow & \color{red}{-9}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+4}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-7x } & = & -11 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & -11 \color{blue}{-4} \\\Leftrightarrow &-9x & = &-15\\\Leftrightarrow & \color{red}{-9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+8}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8-x } & = & 6 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 6 \color{blue}{-8} \\\Leftrightarrow &-15x & = &-2\\\Leftrightarrow & \color{red}{-15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-1}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1-x } & = & -15 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -15 \color{blue}{+1} \\\Leftrightarrow &11x & = &-14\\\Leftrightarrow & \color{red}{11}x & = &-14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-15}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15-5x } & = & 15 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 15 \color{blue}{+15} \\\Leftrightarrow &x & = &30\\\Leftrightarrow & \color{red}{}x & = &30\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 30 \\\Leftrightarrow & \color{green}{ x = 30 } & & \\ & V = \left\{ 30 \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+14}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-x } & = & -8 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -8 \color{blue}{-14} \\\Leftrightarrow &-7x & = &-22\\\Leftrightarrow & \color{red}{-7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{22}{7} } & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+11}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11-x } & = & -6 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -6 \color{blue}{-11} \\\Leftrightarrow &-7x & = &-17\\\Leftrightarrow & \color{red}{-7}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{-7}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7+13x } & = & -5 \color{red}{ -13x }\color{blue}{+7+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -5 \color{blue}{+7} \\\Leftrightarrow &20x & = &2\\\Leftrightarrow & \color{red}{20}x & = &2\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{2}{20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)