Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{5}{11})& = & 9x+\frac{4}{9} \\\Leftrightarrow & -8x+\frac{10}{11}& = & 9x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{+90} & = & \color{red}{891x} +44 \\\Leftrightarrow & -792x \color{red}{+90} \color{blue}{-90} \color{blue}{-891x} & = & \color{red}{891x} +44 \color{blue}{-891x} \color{blue}{-90} \\\Leftrightarrow & -792x-891x& = & 44-90 \\\Leftrightarrow & \color{red}{-1683} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{-1683} & & \\\Leftrightarrow & x = \frac{46}{1683} & & \\ & V = \left\{ \frac{46}{1683} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{4}{9})& = & 7x+\frac{9}{8} \\\Leftrightarrow & -10x+\frac{8}{9}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-720}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} })& = & (\frac{504}{ \color{blue}{72} }x+ \frac{81}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -720x \color{red}{+64} & = & \color{red}{504x} +81 \\\Leftrightarrow & -720x \color{red}{+64} \color{blue}{-64} \color{blue}{-504x} & = & \color{red}{504x} +81 \color{blue}{-504x} \color{blue}{-64} \\\Leftrightarrow & -720x-504x& = & 81-64 \\\Leftrightarrow & \color{red}{-1224} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-1224} & & \\\Leftrightarrow & x = \frac{-1}{72} & & \\ & V = \left\{ \frac{-1}{72} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{11})& = & -5x+\frac{3}{8} \\\Leftrightarrow & -12x+\frac{6}{11}& = & -5x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1056}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1056x \color{red}{+48} & = & \color{red}{-440x} +33 \\\Leftrightarrow & -1056x \color{red}{+48} \color{blue}{-48} \color{blue}{+440x} & = & \color{red}{-440x} +33 \color{blue}{+440x} \color{blue}{-48} \\\Leftrightarrow & -1056x+440x& = & 33-48 \\\Leftrightarrow & \color{red}{-616} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-616} & & \\\Leftrightarrow & x = \frac{15}{616} & & \\ & V = \left\{ \frac{15}{616} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{11})& = & 3x+\frac{4}{11} \\\Leftrightarrow & 10x-\frac{10}{11}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{110}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 110x \color{red}{-10} & = & \color{red}{33x} +4 \\\Leftrightarrow & 110x \color{red}{-10} \color{blue}{+10} \color{blue}{-33x} & = & \color{red}{33x} +4 \color{blue}{-33x} \color{blue}{+10} \\\Leftrightarrow & 110x-33x& = & 4+10 \\\Leftrightarrow & \color{red}{77} x& = & 14 \\\Leftrightarrow & x = \frac{14}{77} & & \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{3}{11})& = & 5x+\frac{3}{7} \\\Leftrightarrow & 24x+\frac{18}{11}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{+126} & = & \color{red}{385x} +33 \\\Leftrightarrow & 1848x \color{red}{+126} \color{blue}{-126} \color{blue}{-385x} & = & \color{red}{385x} +33 \color{blue}{-385x} \color{blue}{-126} \\\Leftrightarrow & 1848x-385x& = & 33-126 \\\Leftrightarrow & \color{red}{1463} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{1463} & & \\ & V = \left\{ \frac{-93}{1463} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{4}{5})& = & 7x+\frac{10}{11} \\\Leftrightarrow & 9x-\frac{12}{5}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{495}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 495x \color{red}{-132} & = & \color{red}{385x} +50 \\\Leftrightarrow & 495x \color{red}{-132} \color{blue}{+132} \color{blue}{-385x} & = & \color{red}{385x} +50 \color{blue}{-385x} \color{blue}{+132} \\\Leftrightarrow & 495x-385x& = & 50+132 \\\Leftrightarrow & \color{red}{110} x& = & 182 \\\Leftrightarrow & x = \frac{182}{110} & & \\\Leftrightarrow & x = \frac{91}{55} & & \\ & V = \left\{ \frac{91}{55} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{4}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -24x-\frac{24}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{-168} & = & \color{red}{175x} +50 \\\Leftrightarrow & -840x \color{red}{-168} \color{blue}{+168} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{+168} \\\Leftrightarrow & -840x-175x& = & 50+168 \\\Leftrightarrow & \color{red}{-1015} x& = & 218 \\\Leftrightarrow & x = \frac{218}{-1015} & & \\\Leftrightarrow & x = \frac{-218}{1015} & & \\ & V = \left\{ \frac{-218}{1015} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{7})& = & -2x+\frac{4}{9} \\\Leftrightarrow & 15x-\frac{20}{7}& = & -2x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{-126}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{-180} & = & \color{red}{-126x} +28 \\\Leftrightarrow & 945x \color{red}{-180} \color{blue}{+180} \color{blue}{+126x} & = & \color{red}{-126x} +28 \color{blue}{+126x} \color{blue}{+180} \\\Leftrightarrow & 945x+126x& = & 28+180 \\\Leftrightarrow & \color{red}{1071} x& = & 208 \\\Leftrightarrow & x = \frac{208}{1071} & & \\ & V = \left\{ \frac{208}{1071} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{2}{5})& = & 5x+\frac{5}{12} \\\Leftrightarrow & -24x-\frac{12}{5}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1440}{ \color{blue}{60} }x- \frac{144}{ \color{blue}{60} })& = & (\frac{300}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1440x \color{red}{-144} & = & \color{red}{300x} +25 \\\Leftrightarrow & -1440x \color{red}{-144} \color{blue}{+144} \color{blue}{-300x} & = & \color{red}{300x} +25 \color{blue}{-300x} \color{blue}{+144} \\\Leftrightarrow & -1440x-300x& = & 25+144 \\\Leftrightarrow & \color{red}{-1740} x& = & 169 \\\Leftrightarrow & x = \frac{169}{-1740} & & \\\Leftrightarrow & x = \frac{-169}{1740} & & \\ & V = \left\{ \frac{-169}{1740} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{5})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -6x-\frac{12}{5}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{-12} & = & \color{red}{-35x} +4 \\\Leftrightarrow & -30x \color{red}{-12} \color{blue}{+12} \color{blue}{+35x} & = & \color{red}{-35x} +4 \color{blue}{+35x} \color{blue}{+12} \\\Leftrightarrow & -30x+35x& = & 4+12 \\\Leftrightarrow & \color{red}{5} x& = & 16 \\\Leftrightarrow & x = \frac{16}{5} & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & 4x+\frac{7}{8} \\\Leftrightarrow & 21x-\frac{14}{3}& = & 4x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{504}{ \color{blue}{24} }x- \frac{112}{ \color{blue}{24} })& = & (\frac{96}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 504x \color{red}{-112} & = & \color{red}{96x} +21 \\\Leftrightarrow & 504x \color{red}{-112} \color{blue}{+112} \color{blue}{-96x} & = & \color{red}{96x} +21 \color{blue}{-96x} \color{blue}{+112} \\\Leftrightarrow & 504x-96x& = & 21+112 \\\Leftrightarrow & \color{red}{408} x& = & 133 \\\Leftrightarrow & x = \frac{133}{408} & & \\ & V = \left\{ \frac{133}{408} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{3})& = & 5x+\frac{9}{4} \\\Leftrightarrow & -12x-\frac{20}{3}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-144}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -144x \color{red}{-80} & = & \color{red}{60x} +27 \\\Leftrightarrow & -144x \color{red}{-80} \color{blue}{+80} \color{blue}{-60x} & = & \color{red}{60x} +27 \color{blue}{-60x} \color{blue}{+80} \\\Leftrightarrow & -144x-60x& = & 27+80 \\\Leftrightarrow & \color{red}{-204} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-204} & & \\\Leftrightarrow & x = \frac{-107}{204} & & \\ & V = \left\{ \frac{-107}{204} \right\} & \\\end{align}\)