Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{11})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 12x-\frac{12}{11}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-60} & = & \color{red}{-275x} +88 \\\Leftrightarrow & 660x \color{red}{-60} \color{blue}{+60} \color{blue}{+275x} & = & \color{red}{-275x} +88 \color{blue}{+275x} \color{blue}{+60} \\\Leftrightarrow & 660x+275x& = & 88+60 \\\Leftrightarrow & \color{red}{935} x& = & 148 \\\Leftrightarrow & x = \frac{148}{935} & & \\ & V = \left\{ \frac{148}{935} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{4}{11})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x-\frac{16}{11}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{80}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-80} & = & \color{red}{275x} +66 \\\Leftrightarrow & -660x \color{red}{-80} \color{blue}{+80} \color{blue}{-275x} & = & \color{red}{275x} +66 \color{blue}{-275x} \color{blue}{+80} \\\Leftrightarrow & -660x-275x& = & 66+80 \\\Leftrightarrow & \color{red}{-935} x& = & 146 \\\Leftrightarrow & x = \frac{146}{-935} & & \\\Leftrightarrow & x = \frac{-146}{935} & & \\ & V = \left\{ \frac{-146}{935} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{2})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -6x+\frac{15}{2}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-132}{ \color{blue}{22} }x+ \frac{165}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{16}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -132x \color{red}{+165} & = & \color{red}{154x} +16 \\\Leftrightarrow & -132x \color{red}{+165} \color{blue}{-165} \color{blue}{-154x} & = & \color{red}{154x} +16 \color{blue}{-154x} \color{blue}{-165} \\\Leftrightarrow & -132x-154x& = & 16-165 \\\Leftrightarrow & \color{red}{-286} x& = & -149 \\\Leftrightarrow & x = \frac{-149}{-286} & & \\\Leftrightarrow & x = \frac{149}{286} & & \\ & V = \left\{ \frac{149}{286} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{9})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -16x+\frac{8}{9}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1008}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1008x \color{red}{+56} & = & \color{red}{-441x} +36 \\\Leftrightarrow & -1008x \color{red}{+56} \color{blue}{-56} \color{blue}{+441x} & = & \color{red}{-441x} +36 \color{blue}{+441x} \color{blue}{-56} \\\Leftrightarrow & -1008x+441x& = & 36-56 \\\Leftrightarrow & \color{red}{-567} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-567} & & \\\Leftrightarrow & x = \frac{20}{567} & & \\ & V = \left\{ \frac{20}{567} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{4}{7})& = & -3x+\frac{8}{9} \\\Leftrightarrow & 28x-4& = & -3x+\frac{8}{9} \\ & & & \text{kgv van noemers 1 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{252}{ \color{blue}{9} }x- \frac{36}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 252x \color{red}{-36} & = & \color{red}{-27x} +8 \\\Leftrightarrow & 252x \color{red}{-36} \color{blue}{+36} \color{blue}{+27x} & = & \color{red}{-27x} +8 \color{blue}{+27x} \color{blue}{+36} \\\Leftrightarrow & 252x+27x& = & 8+36 \\\Leftrightarrow & \color{red}{279} x& = & 44 \\\Leftrightarrow & x = \frac{44}{279} & & \\ & V = \left\{ \frac{44}{279} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{3}{8})& = & -3x+\frac{4}{11} \\\Leftrightarrow & -35x+\frac{21}{8}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-3080}{ \color{blue}{88} }x+ \frac{231}{ \color{blue}{88} })& = & (\frac{-264}{ \color{blue}{88} }x+ \frac{32}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -3080x \color{red}{+231} & = & \color{red}{-264x} +32 \\\Leftrightarrow & -3080x \color{red}{+231} \color{blue}{-231} \color{blue}{+264x} & = & \color{red}{-264x} +32 \color{blue}{+264x} \color{blue}{-231} \\\Leftrightarrow & -3080x+264x& = & 32-231 \\\Leftrightarrow & \color{red}{-2816} x& = & -199 \\\Leftrightarrow & x = \frac{-199}{-2816} & & \\\Leftrightarrow & x = \frac{199}{2816} & & \\ & V = \left\{ \frac{199}{2816} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{3}{8})& = & 2x+\frac{2}{9} \\\Leftrightarrow & 15x-\frac{15}{8}& = & 2x+\frac{2}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1080}{ \color{blue}{72} }x- \frac{135}{ \color{blue}{72} })& = & (\frac{144}{ \color{blue}{72} }x+ \frac{16}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1080x \color{red}{-135} & = & \color{red}{144x} +16 \\\Leftrightarrow & 1080x \color{red}{-135} \color{blue}{+135} \color{blue}{-144x} & = & \color{red}{144x} +16 \color{blue}{-144x} \color{blue}{+135} \\\Leftrightarrow & 1080x-144x& = & 16+135 \\\Leftrightarrow & \color{red}{936} x& = & 151 \\\Leftrightarrow & x = \frac{151}{936} & & \\ & V = \left\{ \frac{151}{936} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{5}{11})& = & 8x+\frac{9}{2} \\\Leftrightarrow & -15x+\frac{25}{11}& = & 8x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-330}{ \color{blue}{22} }x+ \frac{50}{ \color{blue}{22} })& = & (\frac{176}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -330x \color{red}{+50} & = & \color{red}{176x} +99 \\\Leftrightarrow & -330x \color{red}{+50} \color{blue}{-50} \color{blue}{-176x} & = & \color{red}{176x} +99 \color{blue}{-176x} \color{blue}{-50} \\\Leftrightarrow & -330x-176x& = & 99-50 \\\Leftrightarrow & \color{red}{-506} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-506} & & \\\Leftrightarrow & x = \frac{-49}{506} & & \\ & V = \left\{ \frac{-49}{506} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{7})& = & 5x+\frac{9}{8} \\\Leftrightarrow & -4x+\frac{10}{7}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-224}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -224x \color{red}{+80} & = & \color{red}{280x} +63 \\\Leftrightarrow & -224x \color{red}{+80} \color{blue}{-80} \color{blue}{-280x} & = & \color{red}{280x} +63 \color{blue}{-280x} \color{blue}{-80} \\\Leftrightarrow & -224x-280x& = & 63-80 \\\Leftrightarrow & \color{red}{-504} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-504} & & \\\Leftrightarrow & x = \frac{17}{504} & & \\ & V = \left\{ \frac{17}{504} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{3}{8})& = & -3x+\frac{6}{7} \\\Leftrightarrow & 25x+\frac{15}{8}& = & -3x+\frac{6}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1400}{ \color{blue}{56} }x+ \frac{105}{ \color{blue}{56} })& = & (\frac{-168}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1400x \color{red}{+105} & = & \color{red}{-168x} +48 \\\Leftrightarrow & 1400x \color{red}{+105} \color{blue}{-105} \color{blue}{+168x} & = & \color{red}{-168x} +48 \color{blue}{+168x} \color{blue}{-105} \\\Leftrightarrow & 1400x+168x& = & 48-105 \\\Leftrightarrow & \color{red}{1568} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{1568} & & \\ & V = \left\{ \frac{-57}{1568} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{2}{7})& = & -8x+\frac{8}{9} \\\Leftrightarrow & -15x+\frac{10}{7}& = & -8x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-945}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-504}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -945x \color{red}{+90} & = & \color{red}{-504x} +56 \\\Leftrightarrow & -945x \color{red}{+90} \color{blue}{-90} \color{blue}{+504x} & = & \color{red}{-504x} +56 \color{blue}{+504x} \color{blue}{-90} \\\Leftrightarrow & -945x+504x& = & 56-90 \\\Leftrightarrow & \color{red}{-441} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-441} & & \\\Leftrightarrow & x = \frac{34}{441} & & \\ & V = \left\{ \frac{34}{441} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{2}{3})& = & 4x+\frac{7}{11} \\\Leftrightarrow & 35x+\frac{14}{3}& = & 4x+\frac{7}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{21}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{+154} & = & \color{red}{132x} +21 \\\Leftrightarrow & 1155x \color{red}{+154} \color{blue}{-154} \color{blue}{-132x} & = & \color{red}{132x} +21 \color{blue}{-132x} \color{blue}{-154} \\\Leftrightarrow & 1155x-132x& = & 21-154 \\\Leftrightarrow & \color{red}{1023} x& = & -133 \\\Leftrightarrow & x = \frac{-133}{1023} & & \\ & V = \left\{ \frac{-133}{1023} \right\} & \\\end{align}\)