Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-3}& = & -14 \color{red}{ -15x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3+15x } & = & -14 \color{red}{ -15x }\color{blue}{+3+15x } \\\Leftrightarrow & 13x \color{blue}{+15x } & = & -14 \color{blue}{+3} \\\Leftrightarrow &28x & = &-11\\\Leftrightarrow & \color{red}{28}x & = &-11\\\Leftrightarrow & \frac{\color{red}{28}x}{ \color{blue}{ 28}} & = & \frac{-11}{28} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{28} } & & \\ & V = \left\{ \frac{-11}{28} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+5}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+5}\color{blue}{-5-9x } & = & -12 \color{red}{ +9x }\color{blue}{-5-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -12 \color{blue}{-5} \\\Leftrightarrow &-17x & = &-17\\\Leftrightarrow & \color{red}{-17}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-17}{-17} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+5}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+5}\color{blue}{-5-x } & = & -7 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -7 \color{blue}{-5} \\\Leftrightarrow &-9x & = &-12\\\Leftrightarrow & \color{red}{-9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-12}& = & -9 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12+2x } & = & -9 \color{red}{ -2x }\color{blue}{+12+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -9 \color{blue}{+12} \\\Leftrightarrow &13x & = &3\\\Leftrightarrow & \color{red}{13}x & = &3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+7}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7+11x } & = & -7 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -7 \color{blue}{-7} \\\Leftrightarrow &26x & = &-14\\\Leftrightarrow & \color{red}{26}x & = &-14\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-14}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+10}& = & 15 \color{red}{ +2x } \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10-2x } & = & 15 \color{red}{ +2x }\color{blue}{-10-2x } \\\Leftrightarrow & 11x \color{blue}{-2x } & = & 15 \color{blue}{-10} \\\Leftrightarrow &9x & = &5\\\Leftrightarrow & \color{red}{9}x & = &5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-12}& = & -14 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-12}\color{blue}{+12+15x } & = & -14 \color{red}{ -15x }\color{blue}{+12+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &23x & = &-2\\\Leftrightarrow & \color{red}{23}x & = &-2\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-2}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{23} } & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+15}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15-x } & = & 14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 14 \color{blue}{-15} \\\Leftrightarrow &-6x & = &-1\\\Leftrightarrow & \color{red}{-6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-4}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4-7x } & = & 7 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & 7 \color{blue}{+4} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{+1}& = & 3 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1+7x } & = & 3 \color{red}{ -7x }\color{blue}{-1+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 3 \color{blue}{-1} \\\Leftrightarrow &11x & = &2\\\Leftrightarrow & \color{red}{11}x & = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+4}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-x } & = & 15 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 15 \color{blue}{-4} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+10}& = & -12 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+10}\color{blue}{-10+3x } & = & -12 \color{red}{ -3x }\color{blue}{-10+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -12 \color{blue}{-10} \\\Leftrightarrow &7x & = &-22\\\Leftrightarrow & \color{red}{7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)