Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & -8x+\frac{9}{7} \\\Leftrightarrow & 21x-\frac{14}{3}& = & -8x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{441}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 441x \color{red}{-98} & = & \color{red}{-168x} +27 \\\Leftrightarrow & 441x \color{red}{-98} \color{blue}{+98} \color{blue}{+168x} & = & \color{red}{-168x} +27 \color{blue}{+168x} \color{blue}{+98} \\\Leftrightarrow & 441x+168x& = & 27+98 \\\Leftrightarrow & \color{red}{609} x& = & 125 \\\Leftrightarrow & x = \frac{125}{609} & & \\ & V = \left\{ \frac{125}{609} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{9})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -4x+\frac{4}{9}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-396}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -396x \color{red}{+44} & = & \color{red}{-891x} +54 \\\Leftrightarrow & -396x \color{red}{+44} \color{blue}{-44} \color{blue}{+891x} & = & \color{red}{-891x} +54 \color{blue}{+891x} \color{blue}{-44} \\\Leftrightarrow & -396x+891x& = & 54-44 \\\Leftrightarrow & \color{red}{495} x& = & 10 \\\Leftrightarrow & x = \frac{10}{495} & & \\\Leftrightarrow & x = \frac{2}{99} & & \\ & V = \left\{ \frac{2}{99} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{11})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -28x-\frac{35}{11}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x- \frac{105}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{-105} & = & \color{red}{-297x} +44 \\\Leftrightarrow & -924x \color{red}{-105} \color{blue}{+105} \color{blue}{+297x} & = & \color{red}{-297x} +44 \color{blue}{+297x} \color{blue}{+105} \\\Leftrightarrow & -924x+297x& = & 44+105 \\\Leftrightarrow & \color{red}{-627} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-627} & & \\\Leftrightarrow & x = \frac{-149}{627} & & \\ & V = \left\{ \frac{-149}{627} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{3})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -10x-\frac{4}{3}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{28}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-28} & = & \color{red}{147x} +30 \\\Leftrightarrow & -210x \color{red}{-28} \color{blue}{+28} \color{blue}{-147x} & = & \color{red}{147x} +30 \color{blue}{-147x} \color{blue}{+28} \\\Leftrightarrow & -210x-147x& = & 30+28 \\\Leftrightarrow & \color{red}{-357} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-357} & & \\\Leftrightarrow & x = \frac{-58}{357} & & \\ & V = \left\{ \frac{-58}{357} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{3}{5})& = & 5x+\frac{9}{4} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{-48} & = & \color{red}{100x} +45 \\\Leftrightarrow & -240x \color{red}{-48} \color{blue}{+48} \color{blue}{-100x} & = & \color{red}{100x} +45 \color{blue}{-100x} \color{blue}{+48} \\\Leftrightarrow & -240x-100x& = & 45+48 \\\Leftrightarrow & \color{red}{-340} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-340} & & \\\Leftrightarrow & x = \frac{-93}{340} & & \\ & V = \left\{ \frac{-93}{340} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{4}{7})& = & -9x+\frac{3}{11} \\\Leftrightarrow & 8x+\frac{8}{7}& = & -9x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{+88} & = & \color{red}{-693x} +21 \\\Leftrightarrow & 616x \color{red}{+88} \color{blue}{-88} \color{blue}{+693x} & = & \color{red}{-693x} +21 \color{blue}{+693x} \color{blue}{-88} \\\Leftrightarrow & 616x+693x& = & 21-88 \\\Leftrightarrow & \color{red}{1309} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{1309} & & \\ & V = \left\{ \frac{-67}{1309} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{8})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -10x+\frac{25}{8}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-80}{ \color{blue}{8} }x+ \frac{25}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{12}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -80x \color{red}{+25} & = & \color{red}{-56x} +12 \\\Leftrightarrow & -80x \color{red}{+25} \color{blue}{-25} \color{blue}{+56x} & = & \color{red}{-56x} +12 \color{blue}{+56x} \color{blue}{-25} \\\Leftrightarrow & -80x+56x& = & 12-25 \\\Leftrightarrow & \color{red}{-24} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-24} & & \\\Leftrightarrow & x = \frac{13}{24} & & \\ & V = \left\{ \frac{13}{24} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{11})& = & 6x+\frac{8}{5} \\\Leftrightarrow & -18x-\frac{18}{11}& = & 6x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{330}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{-90} & = & \color{red}{330x} +88 \\\Leftrightarrow & -990x \color{red}{-90} \color{blue}{+90} \color{blue}{-330x} & = & \color{red}{330x} +88 \color{blue}{-330x} \color{blue}{+90} \\\Leftrightarrow & -990x-330x& = & 88+90 \\\Leftrightarrow & \color{red}{-1320} x& = & 178 \\\Leftrightarrow & x = \frac{178}{-1320} & & \\\Leftrightarrow & x = \frac{-89}{660} & & \\ & V = \left\{ \frac{-89}{660} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{1}{3})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -35x+\frac{7}{3}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-105}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -105x \color{red}{+7} & = & \color{red}{-9x} +8 \\\Leftrightarrow & -105x \color{red}{+7} \color{blue}{-7} \color{blue}{+9x} & = & \color{red}{-9x} +8 \color{blue}{+9x} \color{blue}{-7} \\\Leftrightarrow & -105x+9x& = & 8-7 \\\Leftrightarrow & \color{red}{-96} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-96} & & \\\Leftrightarrow & x = \frac{-1}{96} & & \\ & V = \left\{ \frac{-1}{96} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{3}{2})& = & -5x+\frac{8}{11} \\\Leftrightarrow & 6x-\frac{9}{2}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{132}{ \color{blue}{22} }x- \frac{99}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{16}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 132x \color{red}{-99} & = & \color{red}{-110x} +16 \\\Leftrightarrow & 132x \color{red}{-99} \color{blue}{+99} \color{blue}{+110x} & = & \color{red}{-110x} +16 \color{blue}{+110x} \color{blue}{+99} \\\Leftrightarrow & 132x+110x& = & 16+99 \\\Leftrightarrow & \color{red}{242} x& = & 115 \\\Leftrightarrow & x = \frac{115}{242} & & \\ & V = \left\{ \frac{115}{242} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{7})& = & 3x+\frac{2}{5} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 3x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{-50} & = & \color{red}{105x} +14 \\\Leftrightarrow & 350x \color{red}{-50} \color{blue}{+50} \color{blue}{-105x} & = & \color{red}{105x} +14 \color{blue}{-105x} \color{blue}{+50} \\\Leftrightarrow & 350x-105x& = & 14+50 \\\Leftrightarrow & \color{red}{245} x& = & 64 \\\Leftrightarrow & x = \frac{64}{245} & & \\ & V = \left\{ \frac{64}{245} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{4})& = & -6x+\frac{5}{2} \\\Leftrightarrow & 35x-\frac{35}{4}& = & -6x+\frac{5}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{140}{ \color{blue}{4} }x- \frac{35}{ \color{blue}{4} })& = & (\frac{-24}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 140x \color{red}{-35} & = & \color{red}{-24x} +10 \\\Leftrightarrow & 140x \color{red}{-35} \color{blue}{+35} \color{blue}{+24x} & = & \color{red}{-24x} +10 \color{blue}{+24x} \color{blue}{+35} \\\Leftrightarrow & 140x+24x& = & 10+35 \\\Leftrightarrow & \color{red}{164} x& = & 45 \\\Leftrightarrow & x = \frac{45}{164} & & \\ & V = \left\{ \frac{45}{164} \right\} & \\\end{align}\)