Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{2}{3})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -6x-\frac{4}{3}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-18}{ \color{blue}{3} }x- \frac{4}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -18x \color{red}{-4} & = & \color{red}{21x} +4 \\\Leftrightarrow & -18x \color{red}{-4} \color{blue}{+4} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{+4} \\\Leftrightarrow & -18x-21x& = & 4+4 \\\Leftrightarrow & \color{red}{-39} x& = & 8 \\\Leftrightarrow & x = \frac{8}{-39} & & \\\Leftrightarrow & x = \frac{-8}{39} & & \\ & V = \left\{ \frac{-8}{39} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{3}{2})& = & 3x+\frac{10}{11} \\\Leftrightarrow & 28x+\frac{21}{2}& = & 3x+\frac{10}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{616}{ \color{blue}{22} }x+ \frac{231}{ \color{blue}{22} })& = & (\frac{66}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 616x \color{red}{+231} & = & \color{red}{66x} +20 \\\Leftrightarrow & 616x \color{red}{+231} \color{blue}{-231} \color{blue}{-66x} & = & \color{red}{66x} +20 \color{blue}{-66x} \color{blue}{-231} \\\Leftrightarrow & 616x-66x& = & 20-231 \\\Leftrightarrow & \color{red}{550} x& = & -211 \\\Leftrightarrow & x = \frac{-211}{550} & & \\ & V = \left\{ \frac{-211}{550} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{3})& = & -3x+\frac{5}{7} \\\Leftrightarrow & 4x-\frac{8}{3}& = & -3x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{-56} & = & \color{red}{-63x} +15 \\\Leftrightarrow & 84x \color{red}{-56} \color{blue}{+56} \color{blue}{+63x} & = & \color{red}{-63x} +15 \color{blue}{+63x} \color{blue}{+56} \\\Leftrightarrow & 84x+63x& = & 15+56 \\\Leftrightarrow & \color{red}{147} x& = & 71 \\\Leftrightarrow & x = \frac{71}{147} & & \\ & V = \left\{ \frac{71}{147} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{2}{7})& = & -3x+\frac{2}{9} \\\Leftrightarrow & -20x+\frac{10}{7}& = & -3x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{+90} & = & \color{red}{-189x} +14 \\\Leftrightarrow & -1260x \color{red}{+90} \color{blue}{-90} \color{blue}{+189x} & = & \color{red}{-189x} +14 \color{blue}{+189x} \color{blue}{-90} \\\Leftrightarrow & -1260x+189x& = & 14-90 \\\Leftrightarrow & \color{red}{-1071} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{-1071} & & \\\Leftrightarrow & x = \frac{76}{1071} & & \\ & V = \left\{ \frac{76}{1071} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{2}{7})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 15x-\frac{10}{7}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{-50} & = & \color{red}{245x} +28 \\\Leftrightarrow & 525x \color{red}{-50} \color{blue}{+50} \color{blue}{-245x} & = & \color{red}{245x} +28 \color{blue}{-245x} \color{blue}{+50} \\\Leftrightarrow & 525x-245x& = & 28+50 \\\Leftrightarrow & \color{red}{280} x& = & 78 \\\Leftrightarrow & x = \frac{78}{280} & & \\\Leftrightarrow & x = \frac{39}{140} & & \\ & V = \left\{ \frac{39}{140} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{4}{3})& = & 3x+\frac{9}{4} \\\Leftrightarrow & -28x+\frac{28}{3}& = & 3x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-336}{ \color{blue}{12} }x+ \frac{112}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -336x \color{red}{+112} & = & \color{red}{36x} +27 \\\Leftrightarrow & -336x \color{red}{+112} \color{blue}{-112} \color{blue}{-36x} & = & \color{red}{36x} +27 \color{blue}{-36x} \color{blue}{-112} \\\Leftrightarrow & -336x-36x& = & 27-112 \\\Leftrightarrow & \color{red}{-372} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{-372} & & \\\Leftrightarrow & x = \frac{85}{372} & & \\ & V = \left\{ \frac{85}{372} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{4}{11})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 9x+\frac{12}{11}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{693}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 693x \color{red}{+84} & = & \color{red}{385x} +44 \\\Leftrightarrow & 693x \color{red}{+84} \color{blue}{-84} \color{blue}{-385x} & = & \color{red}{385x} +44 \color{blue}{-385x} \color{blue}{-84} \\\Leftrightarrow & 693x-385x& = & 44-84 \\\Leftrightarrow & \color{red}{308} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{308} & & \\\Leftrightarrow & x = \frac{-10}{77} & & \\ & V = \left\{ \frac{-10}{77} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{12})& = & 2x+\frac{4}{5} \\\Leftrightarrow & 35x+\frac{35}{12}& = & 2x+\frac{4}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{2100}{ \color{blue}{60} }x+ \frac{175}{ \color{blue}{60} })& = & (\frac{120}{ \color{blue}{60} }x+ \frac{48}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 2100x \color{red}{+175} & = & \color{red}{120x} +48 \\\Leftrightarrow & 2100x \color{red}{+175} \color{blue}{-175} \color{blue}{-120x} & = & \color{red}{120x} +48 \color{blue}{-120x} \color{blue}{-175} \\\Leftrightarrow & 2100x-120x& = & 48-175 \\\Leftrightarrow & \color{red}{1980} x& = & -127 \\\Leftrightarrow & x = \frac{-127}{1980} & & \\ & V = \left\{ \frac{-127}{1980} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{3}{11})& = & 5x+\frac{2}{9} \\\Leftrightarrow & -12x+\frac{18}{11}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x+ \frac{162}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{+162} & = & \color{red}{495x} +22 \\\Leftrightarrow & -1188x \color{red}{+162} \color{blue}{-162} \color{blue}{-495x} & = & \color{red}{495x} +22 \color{blue}{-495x} \color{blue}{-162} \\\Leftrightarrow & -1188x-495x& = & 22-162 \\\Leftrightarrow & \color{red}{-1683} x& = & -140 \\\Leftrightarrow & x = \frac{-140}{-1683} & & \\\Leftrightarrow & x = \frac{140}{1683} & & \\ & V = \left\{ \frac{140}{1683} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{2})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x+\frac{25}{2}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-100}{ \color{blue}{10} }x+ \frac{125}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -100x \color{red}{+125} & = & \color{red}{-70x} +12 \\\Leftrightarrow & -100x \color{red}{+125} \color{blue}{-125} \color{blue}{+70x} & = & \color{red}{-70x} +12 \color{blue}{+70x} \color{blue}{-125} \\\Leftrightarrow & -100x+70x& = & 12-125 \\\Leftrightarrow & \color{red}{-30} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{-30} & & \\\Leftrightarrow & x = \frac{113}{30} & & \\ & V = \left\{ \frac{113}{30} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{3}{11})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 24x+\frac{18}{11}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x+ \frac{90}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{+90} & = & \color{red}{-275x} +88 \\\Leftrightarrow & 1320x \color{red}{+90} \color{blue}{-90} \color{blue}{+275x} & = & \color{red}{-275x} +88 \color{blue}{+275x} \color{blue}{-90} \\\Leftrightarrow & 1320x+275x& = & 88-90 \\\Leftrightarrow & \color{red}{1595} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{1595} & & \\ & V = \left\{ \frac{-2}{1595} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{2})& = & -9x+\frac{9}{7} \\\Leftrightarrow & 35x-\frac{35}{2}& = & -9x+\frac{9}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{490}{ \color{blue}{14} }x- \frac{245}{ \color{blue}{14} })& = & (\frac{-126}{ \color{blue}{14} }x+ \frac{18}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 490x \color{red}{-245} & = & \color{red}{-126x} +18 \\\Leftrightarrow & 490x \color{red}{-245} \color{blue}{+245} \color{blue}{+126x} & = & \color{red}{-126x} +18 \color{blue}{+126x} \color{blue}{+245} \\\Leftrightarrow & 490x+126x& = & 18+245 \\\Leftrightarrow & \color{red}{616} x& = & 263 \\\Leftrightarrow & x = \frac{263}{616} & & \\ & V = \left\{ \frac{263}{616} \right\} & \\\end{align}\)