Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{3})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 12x+\frac{20}{3}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{36}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 36x \color{red}{+20} & = & \color{red}{15x} +2 \\\Leftrightarrow & 36x \color{red}{+20} \color{blue}{-20} \color{blue}{-15x} & = & \color{red}{15x} +2 \color{blue}{-15x} \color{blue}{-20} \\\Leftrightarrow & 36x-15x& = & 2-20 \\\Leftrightarrow & \color{red}{21} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{21} & & \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{4})& = & 2x+\frac{2}{3} \\\Leftrightarrow & 15x+\frac{15}{4}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{24}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{+45} & = & \color{red}{24x} +8 \\\Leftrightarrow & 180x \color{red}{+45} \color{blue}{-45} \color{blue}{-24x} & = & \color{red}{24x} +8 \color{blue}{-24x} \color{blue}{-45} \\\Leftrightarrow & 180x-24x& = & 8-45 \\\Leftrightarrow & \color{red}{156} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{156} & & \\ & V = \left\{ \frac{-37}{156} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{3}{10})& = & 4x+\frac{10}{3} \\\Leftrightarrow & -15x+\frac{9}{10}& = & 4x+\frac{10}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-450}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} })& = & (\frac{120}{ \color{blue}{30} }x+ \frac{100}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -450x \color{red}{+27} & = & \color{red}{120x} +100 \\\Leftrightarrow & -450x \color{red}{+27} \color{blue}{-27} \color{blue}{-120x} & = & \color{red}{120x} +100 \color{blue}{-120x} \color{blue}{-27} \\\Leftrightarrow & -450x-120x& = & 100-27 \\\Leftrightarrow & \color{red}{-570} x& = & 73 \\\Leftrightarrow & x = \frac{73}{-570} & & \\\Leftrightarrow & x = \frac{-73}{570} & & \\ & V = \left\{ \frac{-73}{570} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{4}{3})& = & -7x+\frac{7}{3} \\\Leftrightarrow & 10x+\frac{8}{3}& = & -7x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{30}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 30x \color{red}{+8} & = & \color{red}{-21x} +7 \\\Leftrightarrow & 30x \color{red}{+8} \color{blue}{-8} \color{blue}{+21x} & = & \color{red}{-21x} +7 \color{blue}{+21x} \color{blue}{-8} \\\Leftrightarrow & 30x+21x& = & 7-8 \\\Leftrightarrow & \color{red}{51} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{51} & & \\ & V = \left\{ \frac{-1}{51} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -6x-\frac{6}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-18} & = & \color{red}{147x} +14 \\\Leftrightarrow & -126x \color{red}{-18} \color{blue}{+18} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{+18} \\\Leftrightarrow & -126x-147x& = & 14+18 \\\Leftrightarrow & \color{red}{-273} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-273} & & \\\Leftrightarrow & x = \frac{-32}{273} & & \\ & V = \left\{ \frac{-32}{273} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{4}{9})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -25x+\frac{20}{9}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-225}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -225x \color{red}{+20} & = & \color{red}{63x} +10 \\\Leftrightarrow & -225x \color{red}{+20} \color{blue}{-20} \color{blue}{-63x} & = & \color{red}{63x} +10 \color{blue}{-63x} \color{blue}{-20} \\\Leftrightarrow & -225x-63x& = & 10-20 \\\Leftrightarrow & \color{red}{-288} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-288} & & \\\Leftrightarrow & x = \frac{5}{144} & & \\ & V = \left\{ \frac{5}{144} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{5})& = & -2x+\frac{9}{4} \\\Leftrightarrow & 9x-\frac{9}{5}& = & -2x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{180}{ \color{blue}{20} }x- \frac{36}{ \color{blue}{20} })& = & (\frac{-40}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 180x \color{red}{-36} & = & \color{red}{-40x} +45 \\\Leftrightarrow & 180x \color{red}{-36} \color{blue}{+36} \color{blue}{+40x} & = & \color{red}{-40x} +45 \color{blue}{+40x} \color{blue}{+36} \\\Leftrightarrow & 180x+40x& = & 45+36 \\\Leftrightarrow & \color{red}{220} x& = & 81 \\\Leftrightarrow & x = \frac{81}{220} & & \\ & V = \left\{ \frac{81}{220} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{5}{2})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -25x+\frac{25}{2}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 2 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-250}{ \color{blue}{10} }x+ \frac{125}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -250x \color{red}{+125} & = & \color{red}{70x} +3 \\\Leftrightarrow & -250x \color{red}{+125} \color{blue}{-125} \color{blue}{-70x} & = & \color{red}{70x} +3 \color{blue}{-70x} \color{blue}{-125} \\\Leftrightarrow & -250x-70x& = & 3-125 \\\Leftrightarrow & \color{red}{-320} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{-320} & & \\\Leftrightarrow & x = \frac{61}{160} & & \\ & V = \left\{ \frac{61}{160} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{5}{7})& = & 5x+\frac{6}{7} \\\Leftrightarrow & -24x+\frac{30}{7}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-168}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -168x \color{red}{+30} & = & \color{red}{35x} +6 \\\Leftrightarrow & -168x \color{red}{+30} \color{blue}{-30} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{-30} \\\Leftrightarrow & -168x-35x& = & 6-30 \\\Leftrightarrow & \color{red}{-203} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{-203} & & \\\Leftrightarrow & x = \frac{24}{203} & & \\ & V = \left\{ \frac{24}{203} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{9})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 8x+\frac{8}{9}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{+8} & = & \color{red}{-45x} +12 \\\Leftrightarrow & 72x \color{red}{+8} \color{blue}{-8} \color{blue}{+45x} & = & \color{red}{-45x} +12 \color{blue}{+45x} \color{blue}{-8} \\\Leftrightarrow & 72x+45x& = & 12-8 \\\Leftrightarrow & \color{red}{117} x& = & 4 \\\Leftrightarrow & x = \frac{4}{117} & & \\ & V = \left\{ \frac{4}{117} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{4}{11})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 24x-\frac{24}{11}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{528}{ \color{blue}{22} }x- \frac{48}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 528x \color{red}{-48} & = & \color{red}{-110x} +99 \\\Leftrightarrow & 528x \color{red}{-48} \color{blue}{+48} \color{blue}{+110x} & = & \color{red}{-110x} +99 \color{blue}{+110x} \color{blue}{+48} \\\Leftrightarrow & 528x+110x& = & 99+48 \\\Leftrightarrow & \color{red}{638} x& = & 147 \\\Leftrightarrow & x = \frac{147}{638} & & \\ & V = \left\{ \frac{147}{638} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{4}{7})& = & 7x+\frac{8}{7} \\\Leftrightarrow & -16x+\frac{16}{7}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-112}{ \color{blue}{7} }x+ \frac{16}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -112x \color{red}{+16} & = & \color{red}{49x} +8 \\\Leftrightarrow & -112x \color{red}{+16} \color{blue}{-16} \color{blue}{-49x} & = & \color{red}{49x} +8 \color{blue}{-49x} \color{blue}{-16} \\\Leftrightarrow & -112x-49x& = & 8-16 \\\Leftrightarrow & \color{red}{-161} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-161} & & \\\Leftrightarrow & x = \frac{8}{161} & & \\ & V = \left\{ \frac{8}{161} \right\} & \\\end{align}\)