Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -6x-\frac{6}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x- \frac{6}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{-6} & = & \color{red}{35x} +6 \\\Leftrightarrow & -30x \color{red}{-6} \color{blue}{+6} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+6} \\\Leftrightarrow & -30x-35x& = & 6+6 \\\Leftrightarrow & \color{red}{-65} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-65} & & \\\Leftrightarrow & x = \frac{-12}{65} & & \\ & V = \left\{ \frac{-12}{65} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{5}{2})& = & -2x+\frac{10}{7} \\\Leftrightarrow & 21x+\frac{35}{2}& = & -2x+\frac{10}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{294}{ \color{blue}{14} }x+ \frac{245}{ \color{blue}{14} })& = & (\frac{-28}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 294x \color{red}{+245} & = & \color{red}{-28x} +20 \\\Leftrightarrow & 294x \color{red}{+245} \color{blue}{-245} \color{blue}{+28x} & = & \color{red}{-28x} +20 \color{blue}{+28x} \color{blue}{-245} \\\Leftrightarrow & 294x+28x& = & 20-245 \\\Leftrightarrow & \color{red}{322} x& = & -225 \\\Leftrightarrow & x = \frac{-225}{322} & & \\ & V = \left\{ \frac{-225}{322} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{7})& = & 9x+\frac{9}{4} \\\Leftrightarrow & 10x+\frac{8}{7}& = & 9x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{280}{ \color{blue}{28} }x+ \frac{32}{ \color{blue}{28} })& = & (\frac{252}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 280x \color{red}{+32} & = & \color{red}{252x} +63 \\\Leftrightarrow & 280x \color{red}{+32} \color{blue}{-32} \color{blue}{-252x} & = & \color{red}{252x} +63 \color{blue}{-252x} \color{blue}{-32} \\\Leftrightarrow & 280x-252x& = & 63-32 \\\Leftrightarrow & \color{red}{28} x& = & 31 \\\Leftrightarrow & x = \frac{31}{28} & & \\ & V = \left\{ \frac{31}{28} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{3}{2})& = & 8x+\frac{2}{11} \\\Leftrightarrow & -21x-\frac{21}{2}& = & 8x+\frac{2}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-462}{ \color{blue}{22} }x- \frac{231}{ \color{blue}{22} })& = & (\frac{176}{ \color{blue}{22} }x+ \frac{4}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -462x \color{red}{-231} & = & \color{red}{176x} +4 \\\Leftrightarrow & -462x \color{red}{-231} \color{blue}{+231} \color{blue}{-176x} & = & \color{red}{176x} +4 \color{blue}{-176x} \color{blue}{+231} \\\Leftrightarrow & -462x-176x& = & 4+231 \\\Leftrightarrow & \color{red}{-638} x& = & 235 \\\Leftrightarrow & x = \frac{235}{-638} & & \\\Leftrightarrow & x = \frac{-235}{638} & & \\ & V = \left\{ \frac{-235}{638} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 30x-\frac{18}{11}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{660}{ \color{blue}{22} }x- \frac{36}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 660x \color{red}{-36} & = & \color{red}{-154x} +77 \\\Leftrightarrow & 660x \color{red}{-36} \color{blue}{+36} \color{blue}{+154x} & = & \color{red}{-154x} +77 \color{blue}{+154x} \color{blue}{+36} \\\Leftrightarrow & 660x+154x& = & 77+36 \\\Leftrightarrow & \color{red}{814} x& = & 113 \\\Leftrightarrow & x = \frac{113}{814} & & \\ & V = \left\{ \frac{113}{814} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & 5x+\frac{5}{3} \\\Leftrightarrow & -12x-\frac{18}{11}& = & 5x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-54} & = & \color{red}{165x} +55 \\\Leftrightarrow & -396x \color{red}{-54} \color{blue}{+54} \color{blue}{-165x} & = & \color{red}{165x} +55 \color{blue}{-165x} \color{blue}{+54} \\\Leftrightarrow & -396x-165x& = & 55+54 \\\Leftrightarrow & \color{red}{-561} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-561} & & \\\Leftrightarrow & x = \frac{-109}{561} & & \\ & V = \left\{ \frac{-109}{561} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{5})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 6x+\frac{6}{5}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{50x} +15 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{-50x} & = & \color{red}{50x} +15 \color{blue}{-50x} \color{blue}{-12} \\\Leftrightarrow & 60x-50x& = & 15-12 \\\Leftrightarrow & \color{red}{10} x& = & 3 \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{5}{7})& = & 3x+\frac{7}{6} \\\Leftrightarrow & -8x+\frac{10}{7}& = & 3x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-336}{ \color{blue}{42} }x+ \frac{60}{ \color{blue}{42} })& = & (\frac{126}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -336x \color{red}{+60} & = & \color{red}{126x} +49 \\\Leftrightarrow & -336x \color{red}{+60} \color{blue}{-60} \color{blue}{-126x} & = & \color{red}{126x} +49 \color{blue}{-126x} \color{blue}{-60} \\\Leftrightarrow & -336x-126x& = & 49-60 \\\Leftrightarrow & \color{red}{-462} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-462} & & \\\Leftrightarrow & x = \frac{1}{42} & & \\ & V = \left\{ \frac{1}{42} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{4}{7})& = & -6x+\frac{7}{3} \\\Leftrightarrow & 25x-\frac{20}{7}& = & -6x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{525}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-126}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 525x \color{red}{-60} & = & \color{red}{-126x} +49 \\\Leftrightarrow & 525x \color{red}{-60} \color{blue}{+60} \color{blue}{+126x} & = & \color{red}{-126x} +49 \color{blue}{+126x} \color{blue}{+60} \\\Leftrightarrow & 525x+126x& = & 49+60 \\\Leftrightarrow & \color{red}{651} x& = & 109 \\\Leftrightarrow & x = \frac{109}{651} & & \\ & V = \left\{ \frac{109}{651} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{3})& = & 3x+\frac{3}{2} \\\Leftrightarrow & -8x+\frac{8}{3}& = & 3x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{+16} & = & \color{red}{18x} +9 \\\Leftrightarrow & -48x \color{red}{+16} \color{blue}{-16} \color{blue}{-18x} & = & \color{red}{18x} +9 \color{blue}{-18x} \color{blue}{-16} \\\Leftrightarrow & -48x-18x& = & 9-16 \\\Leftrightarrow & \color{red}{-66} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-66} & & \\\Leftrightarrow & x = \frac{7}{66} & & \\ & V = \left\{ \frac{7}{66} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{2}{9})& = & -5x+\frac{8}{11} \\\Leftrightarrow & 12x-\frac{8}{9}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1188}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1188x \color{red}{-88} & = & \color{red}{-495x} +72 \\\Leftrightarrow & 1188x \color{red}{-88} \color{blue}{+88} \color{blue}{+495x} & = & \color{red}{-495x} +72 \color{blue}{+495x} \color{blue}{+88} \\\Leftrightarrow & 1188x+495x& = & 72+88 \\\Leftrightarrow & \color{red}{1683} x& = & 160 \\\Leftrightarrow & x = \frac{160}{1683} & & \\ & V = \left\{ \frac{160}{1683} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{5}{9})& = & 3x+\frac{7}{8} \\\Leftrightarrow & -14x-\frac{35}{9}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1008}{ \color{blue}{72} }x- \frac{280}{ \color{blue}{72} })& = & (\frac{216}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1008x \color{red}{-280} & = & \color{red}{216x} +63 \\\Leftrightarrow & -1008x \color{red}{-280} \color{blue}{+280} \color{blue}{-216x} & = & \color{red}{216x} +63 \color{blue}{-216x} \color{blue}{+280} \\\Leftrightarrow & -1008x-216x& = & 63+280 \\\Leftrightarrow & \color{red}{-1224} x& = & 343 \\\Leftrightarrow & x = \frac{343}{-1224} & & \\\Leftrightarrow & x = \frac{-343}{1224} & & \\ & V = \left\{ \frac{-343}{1224} \right\} & \\\end{align}\)