Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+1}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1-x } & = & -14 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -14 \color{blue}{-1} \\\Leftrightarrow &-11x & = &-15\\\Leftrightarrow & \color{red}{-11}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+7}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7-x } & = & -11 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -11 \color{blue}{-7} \\\Leftrightarrow &7x & = &-18\\\Leftrightarrow & \color{red}{7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-18}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-14}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-9x } & = & -7 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &-17x & = &7\\\Leftrightarrow & \color{red}{-17}x & = &7\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{7}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-12}& = & -13 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-8x } & = & -13 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -13 \color{blue}{+12} \\\Leftrightarrow &-23x & = &-1\\\Leftrightarrow & \color{red}{-23}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-1}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{1}{23} } & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-9}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-x } & = & -14 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -14 \color{blue}{+9} \\\Leftrightarrow &-14x & = &-5\\\Leftrightarrow & \color{red}{-14}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-12}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12-x } & = & -7 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -7 \color{blue}{+12} \\\Leftrightarrow &-10x & = &5\\\Leftrightarrow & \color{red}{-10}x & = &5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{-9}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-9}\color{blue}{+9-5x } & = & -7 \color{red}{ +5x }\color{blue}{+9-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -7 \color{blue}{+9} \\\Leftrightarrow &-17x & = &2\\\Leftrightarrow & \color{red}{-17}x & = &2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+15}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15+13x } & = & 1 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & 1 \color{blue}{-15} \\\Leftrightarrow &21x & = &-14\\\Leftrightarrow & \color{red}{21}x & = &-14\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-14}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-15}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15-11x } & = & -1 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &x & = &14\\\Leftrightarrow & \color{red}{}x & = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+10}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+10}\color{blue}{-10-7x } & = & 10 \color{red}{ +7x }\color{blue}{-10-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 10 \color{blue}{-10} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+13}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+13}\color{blue}{-13-x } & = & -4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -4 \color{blue}{-13} \\\Leftrightarrow &-10x & = &-17\\\Leftrightarrow & \color{red}{-10}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-17}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{17}{10} } & & \\ & V = \left\{ \frac{17}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+1}& = & 15 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1+9x } & = & 15 \color{red}{ -9x }\color{blue}{-1+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & 15 \color{blue}{-1} \\\Leftrightarrow &8x & = &14\\\Leftrightarrow & \color{red}{8}x & = &14\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{14}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)