Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{3}{11})& = & -5x+\frac{7}{10} \\\Leftrightarrow & 18x-\frac{18}{11}& = & -5x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1980}{ \color{blue}{110} }x- \frac{180}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1980x \color{red}{-180} & = & \color{red}{-550x} +77 \\\Leftrightarrow & 1980x \color{red}{-180} \color{blue}{+180} \color{blue}{+550x} & = & \color{red}{-550x} +77 \color{blue}{+550x} \color{blue}{+180} \\\Leftrightarrow & 1980x+550x& = & 77+180 \\\Leftrightarrow & \color{red}{2530} x& = & 257 \\\Leftrightarrow & x = \frac{257}{2530} & & \\ & V = \left\{ \frac{257}{2530} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{4}{3})& = & -7x+\frac{5}{12} \\\Leftrightarrow & 16x+\frac{16}{3}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{192}{ \color{blue}{12} }x+ \frac{64}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 192x \color{red}{+64} & = & \color{red}{-84x} +5 \\\Leftrightarrow & 192x \color{red}{+64} \color{blue}{-64} \color{blue}{+84x} & = & \color{red}{-84x} +5 \color{blue}{+84x} \color{blue}{-64} \\\Leftrightarrow & 192x+84x& = & 5-64 \\\Leftrightarrow & \color{red}{276} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{276} & & \\ & V = \left\{ \frac{-59}{276} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{4}{7})& = & 7x+\frac{2}{9} \\\Leftrightarrow & -20x-\frac{16}{7}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x- \frac{144}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{-144} & = & \color{red}{441x} +14 \\\Leftrightarrow & -1260x \color{red}{-144} \color{blue}{+144} \color{blue}{-441x} & = & \color{red}{441x} +14 \color{blue}{-441x} \color{blue}{+144} \\\Leftrightarrow & -1260x-441x& = & 14+144 \\\Leftrightarrow & \color{red}{-1701} x& = & 158 \\\Leftrightarrow & x = \frac{158}{-1701} & & \\\Leftrightarrow & x = \frac{-158}{1701} & & \\ & V = \left\{ \frac{-158}{1701} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{5}{4})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -6x-\frac{15}{4}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-120}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -120x \color{red}{-75} & = & \color{red}{140x} +24 \\\Leftrightarrow & -120x \color{red}{-75} \color{blue}{+75} \color{blue}{-140x} & = & \color{red}{140x} +24 \color{blue}{-140x} \color{blue}{+75} \\\Leftrightarrow & -120x-140x& = & 24+75 \\\Leftrightarrow & \color{red}{-260} x& = & 99 \\\Leftrightarrow & x = \frac{99}{-260} & & \\\Leftrightarrow & x = \frac{-99}{260} & & \\ & V = \left\{ \frac{-99}{260} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{4}{11})& = & 6x+\frac{3}{4} \\\Leftrightarrow & 35x+\frac{28}{11}& = & 6x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1540}{ \color{blue}{44} }x+ \frac{112}{ \color{blue}{44} })& = & (\frac{264}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1540x \color{red}{+112} & = & \color{red}{264x} +33 \\\Leftrightarrow & 1540x \color{red}{+112} \color{blue}{-112} \color{blue}{-264x} & = & \color{red}{264x} +33 \color{blue}{-264x} \color{blue}{-112} \\\Leftrightarrow & 1540x-264x& = & 33-112 \\\Leftrightarrow & \color{red}{1276} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{1276} & & \\ & V = \left\{ \frac{-79}{1276} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{3}{11})& = & -8x+\frac{6}{7} \\\Leftrightarrow & 21x-\frac{21}{11}& = & -8x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1617}{ \color{blue}{77} }x- \frac{147}{ \color{blue}{77} })& = & (\frac{-616}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1617x \color{red}{-147} & = & \color{red}{-616x} +66 \\\Leftrightarrow & 1617x \color{red}{-147} \color{blue}{+147} \color{blue}{+616x} & = & \color{red}{-616x} +66 \color{blue}{+616x} \color{blue}{+147} \\\Leftrightarrow & 1617x+616x& = & 66+147 \\\Leftrightarrow & \color{red}{2233} x& = & 213 \\\Leftrightarrow & x = \frac{213}{2233} & & \\ & V = \left\{ \frac{213}{2233} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{2}{5})& = & -2x+\frac{10}{3} \\\Leftrightarrow & -28x+\frac{14}{5}& = & -2x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-420}{ \color{blue}{15} }x+ \frac{42}{ \color{blue}{15} })& = & (\frac{-30}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -420x \color{red}{+42} & = & \color{red}{-30x} +50 \\\Leftrightarrow & -420x \color{red}{+42} \color{blue}{-42} \color{blue}{+30x} & = & \color{red}{-30x} +50 \color{blue}{+30x} \color{blue}{-42} \\\Leftrightarrow & -420x+30x& = & 50-42 \\\Leftrightarrow & \color{red}{-390} x& = & 8 \\\Leftrightarrow & x = \frac{8}{-390} & & \\\Leftrightarrow & x = \frac{-4}{195} & & \\ & V = \left\{ \frac{-4}{195} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & 3x+\frac{5}{2} \\\Leftrightarrow & -20x-\frac{16}{7}& = & 3x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x- \frac{32}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{-32} & = & \color{red}{42x} +35 \\\Leftrightarrow & -280x \color{red}{-32} \color{blue}{+32} \color{blue}{-42x} & = & \color{red}{42x} +35 \color{blue}{-42x} \color{blue}{+32} \\\Leftrightarrow & -280x-42x& = & 35+32 \\\Leftrightarrow & \color{red}{-322} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-322} & & \\\Leftrightarrow & x = \frac{-67}{322} & & \\ & V = \left\{ \frac{-67}{322} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{4}{7})& = & 9x+\frac{2}{9} \\\Leftrightarrow & -18x+\frac{24}{7}& = & 9x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1134}{ \color{blue}{63} }x+ \frac{216}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1134x \color{red}{+216} & = & \color{red}{567x} +14 \\\Leftrightarrow & -1134x \color{red}{+216} \color{blue}{-216} \color{blue}{-567x} & = & \color{red}{567x} +14 \color{blue}{-567x} \color{blue}{-216} \\\Leftrightarrow & -1134x-567x& = & 14-216 \\\Leftrightarrow & \color{red}{-1701} x& = & -202 \\\Leftrightarrow & x = \frac{-202}{-1701} & & \\\Leftrightarrow & x = \frac{202}{1701} & & \\ & V = \left\{ \frac{202}{1701} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{2}{11})& = & 6x+\frac{5}{9} \\\Leftrightarrow & 35x+\frac{14}{11}& = & 6x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{3465}{ \color{blue}{99} }x+ \frac{126}{ \color{blue}{99} })& = & (\frac{594}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 3465x \color{red}{+126} & = & \color{red}{594x} +55 \\\Leftrightarrow & 3465x \color{red}{+126} \color{blue}{-126} \color{blue}{-594x} & = & \color{red}{594x} +55 \color{blue}{-594x} \color{blue}{-126} \\\Leftrightarrow & 3465x-594x& = & 55-126 \\\Leftrightarrow & \color{red}{2871} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{2871} & & \\ & V = \left\{ \frac{-71}{2871} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{3}{7})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -10x+\frac{15}{7}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x+ \frac{30}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{+30} & = & \color{red}{-98x} +63 \\\Leftrightarrow & -140x \color{red}{+30} \color{blue}{-30} \color{blue}{+98x} & = & \color{red}{-98x} +63 \color{blue}{+98x} \color{blue}{-30} \\\Leftrightarrow & -140x+98x& = & 63-30 \\\Leftrightarrow & \color{red}{-42} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-42} & & \\\Leftrightarrow & x = \frac{-11}{14} & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{7})& = & 7x+\frac{3}{11} \\\Leftrightarrow & -10x-\frac{10}{7}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{-110} & = & \color{red}{539x} +21 \\\Leftrightarrow & -770x \color{red}{-110} \color{blue}{+110} \color{blue}{-539x} & = & \color{red}{539x} +21 \color{blue}{-539x} \color{blue}{+110} \\\Leftrightarrow & -770x-539x& = & 21+110 \\\Leftrightarrow & \color{red}{-1309} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-1309} & & \\\Leftrightarrow & x = \frac{-131}{1309} & & \\ & V = \left\{ \frac{-131}{1309} \right\} & \\\end{align}\)